Algebraic properties of weak quantum symmetries

This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)representations, and applications in groupoids, path algebras, and Lie algebroids. The research employs algebraic and categorical techniques to explore the foundational properties of these structures, establ...

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Autores:: Calderón Mateus, Fabio Alejandro

Tipo de recurso:: Doctoral thesis

Fecha de publicación:: 2023

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: eng

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dc.title.eng.fl_str_mv	Algebraic properties of weak quantum symmetries
dc.title.translated.spa.fl_str_mv	Propiedades algebraicas de las simetrías cuánticas débiles
title	Algebraic properties of weak quantum symmetries
spellingShingle	Algebraic properties of weak quantum symmetries 510 - Matemáticas::512 - Álgebra Formas matemáticas Forms (mathematics) Monoidal category Weak Hopf algebra Representation theory Groupoid Lie algebroid Path algebra Quiver Álgebra de Hopf débil Categoría monoidal Teoría de representaciones Grupoide Algebroide de Lie Álgebra de caminos Carcaj
title_short	Algebraic properties of weak quantum symmetries
title_full	Algebraic properties of weak quantum symmetries
title_fullStr	Algebraic properties of weak quantum symmetries
title_full_unstemmed	Algebraic properties of weak quantum symmetries
title_sort	Algebraic properties of weak quantum symmetries
dc.creator.fl_str_mv	Calderón Mateus, Fabio Alejandro
dc.contributor.advisor.none.fl_str_mv	Chelsea, Walton Milton Armando, Reyes Villamil
dc.contributor.author.none.fl_str_mv	Calderón Mateus, Fabio Alejandro
dc.contributor.orcid.spa.fl_str_mv	Calderón, Fabio [0000-0003-1777-0805]
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas::512 - Álgebra
topic	510 - Matemáticas::512 - Álgebra Formas matemáticas Forms (mathematics) Monoidal category Weak Hopf algebra Representation theory Groupoid Lie algebroid Path algebra Quiver Álgebra de Hopf débil Categoría monoidal Teoría de representaciones Grupoide Algebroide de Lie Álgebra de caminos Carcaj
dc.subject.lemb.spa.fl_str_mv	Formas matemáticas
dc.subject.lemb.eng.fl_str_mv	Forms (mathematics)
dc.subject.proposal.eng.fl_str_mv	Monoidal category Weak Hopf algebra Representation theory Groupoid Lie algebroid Path algebra Quiver
dc.subject.proposal.spa.fl_str_mv	Álgebra de Hopf débil Categoría monoidal Teoría de representaciones Grupoide Algebroide de Lie Álgebra de caminos Carcaj
description	This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)representations, and applications in groupoids, path algebras, and Lie algebroids. The research employs algebraic and categorical techniques to explore the foundational properties of these structures, establishing connections between algebraic and categorical frameworks, and addressing open problems related to their actions on noncommutative graded algebras. By combining theoretical findings and practical examples, this work enhances our understanding of weak Hopf algebras as symmetry generators and their broader implications in various mathematical contexts. Our results contribute to the field of noncommutative algebra and Hopf algebras, paving the way for future research in these areas. (Texto tomado de la fuente)
publishDate	2023
dc.date.accessioned.none.fl_str_mv	2023-07-31T19:42:30Z
dc.date.available.none.fl_str_mv	2023-07-31T19:42:30Z
dc.date.issued.none.fl_str_mv	2023-07-24
dc.type.spa.fl_str_mv	Trabajo de grado - Doctorado
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dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/84376
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/84376 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	eng
language	eng
dc.relation.references.spa.fl_str_mv	M. Alves, E. Batista, and J. Vercruysse. Partial representations of hopf algebras. J. Algebra, 426:137–187, 2015. N. Andruskiewitsch, W. R. Ferrer-Santos, and H. J. Schneider, editors. New trends in Hopf algebra theory. Proceedings of the Colloquium on Quantum Groups and Hopf Algebras held in La Falda, August 9–13, 1999, volume 267 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 2000. I. Assem, A. Skowronski, and D. Simson. Elements of the representation theory of associative algebras. Vol. 1: Techniques of representation theory, volume 65 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2006. G. Böhm. Hopf Algebras and Their Generalizations from a Category Theoretical Point of View, volume 2226 of Lecture Notes in Mathematics. Springer International Publishing, 2018. Y. Bahturin. Identical Relations in Lie Algebras, volume 68 of De Gruyter Expositions in Mathematics. De Gruyter, sec edition, 2021. Translated from the Russian by Bahturin. G. Böhm, S. Caenepeel, and K. Janssen. Weak bialgebras and monoidal categories. Comm. Algebra, 39(12):4584–4607, 2011. M. Artin, W. Schelter, and J. Tate. Quantum deformations of GLn. Comm. Pure Appl. Math., 44(8-9):879–895, 1991 T. Brzeziński, S. Caenepeel, and G. Militaru. Doi-Koppinen modules for quantum groupoids. J. Pure Appl. Algebra, 175(1-3):45–62, 2002. Special volume celebrating the 70th birthday of Professor Max Kelly. D. Bagio, D. Florez, and A. Paques. Partial actions of ordered groupoids on rings. J. Algebra Appl., 09(3):501–517, 2010. K. A. Brown and K. R. Goodearl. Lectures on Algebraic Quantum Groups. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser Basel, 2002. G. Böhm, J. Gómez-Torrecillas, and E. López-Centella. On the category of weak bialgebras. J. Algebra, 399:801–844, 2014. R. Brown, P. J. Higgins, and R. Sivera. Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids. Number 15 in Tracts in Mathematics. EMS Press, 2011. G. Bôhm, F. Nill, and K. Szlachányi. Weak Hopf algebras. I. Integral theory and C-structure. J. Algebra, 221(2):385–438, 1999. D. Bagio and A. Paques. Partial groupoid actions: Globalization, Morita theory, and Galois theory. Comm. Algebra, 40(10):3658–3678, 2012. M. Brion. Representations of quivers. In Geometric methods in representation theory (I), volume 24 of Séminaires & Congrès: Collection SMF, pages 103–144. Société Mathématique de France, 2012 J. Cuadra, P. Etingof, and C. Walton. Semisimple Hopf actions on Weyl algebras. Adv. Math., 282:47–55, 2015. J. Cuadra, P. Etingof, and C. Walton. Finite dimensional Hopf actions on Weyl algebras. Adv. Math., 302:25–39, 2016. S. Caenepeel and E. De Groot. Modules over weak entwining structures. In N. Andruskiewitsch, W. R. Ferrer-Santos, and H. J. Schneider, editors, New trends in Hopf algebra theory. Proceedings of the Colloquium on Quantum Groups and Hopf Algebras held in La Falda, August 9–13, 1999, volume 267 of Contemp. Math., pages 31–54. Amer. Math. Soc., Providence, RI, 2000. F. Calderón, H. Huang, E. Wicks, and R. Won. Symmetries captured by actions of weak Hopf algebras. arXiv preprint arXiv:2209.11903, 2023. K. Chan, E. Kirkman, C. Walton, and J. J. Zhang. Quantum binary polyhedral groups and their actions on quantum planes. J. Reine Angew. Math., 719:211–252, 2016. F. U. Coelho and S. X. Liu. Generalized path algebras. In F. van Oystaeyen and M. Saorin, editors, Interactions between ring theory and representations of algebras, volume 210 of Lecture Notes in Pure and Applied Mathematics, pages 53–66. CRC, 2000. D. Cheng and F. Li. The structure of weak Hopf algebras corresponding to Uq(sl2). Comm. Algebra, 37(3):729–742, 2009. G. Böhm and K. Szlachányi. Weak C-Hopf algebras: the coassociative symmetry of non-integral dimensions. In R. Budzyński, W. Pusz, and S. Zakrzewski, editors, Quantum groups and quantum spaces (Warsaw, 1995), volume 40 of Banach Center Publ., pages 9–19. Polish Acad. Sci. Inst. Math., Warsaw, 1997. M. Cohen and S. Montgomery. Group-graded rings, smash products, and group actions. Trans. Amer. Math. Soc., 282(1):237–258, 1984. F. Castro, A. Paques, G. Quadros, and A. Sant’Ana. Partial actions of weak Hopf algebras: Smash product, globalization and Morita theory. J. Pure Appl. Algebra, 219(12):5511–5538, 2015. F. Calderón and A. Reyes. On the (partial) representation category of weak Hopf algebras. In preparation, 2023. F. Calderón and C. Walton. Algebraic properties of face algebras. J. Algebra Appl., 22(03):2350076, 2023. S. Dăscălescu, C. Năstăsescu, and Ş. Raianu. Hopf Algebras: An Introduction, volume 235 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., first edition, 2001. M. Dokuchaev. Recent developments around partial actions. São Paulo J. Math. Sci., 13(1):195–247, 2018. B. Day and C. Pastro. Note on Frobenius monoidal functors. New York J. Math., 14:733–742, 2008. P. Etingof and C. H. Eu. Koszulity and the Hilbert series of preprojective algebras. Math. Res. Lett., 14(4):589–596, 2007. P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik. Tensor categories, volume 205 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2015. S. Eilenberg and T. Nakayama. On the dimension of modules and algebras, II: Frobenius algebras and quasi-Frobenius rings. Nagoya Math. J., 9:1–16, 1955. P. Etingof and C. Walton. Semisimple Hopf actions on commutative domains. Adv. Math., 251:47–61, 2014. P. Etingof and C. Walton. Finite dimensional Hopf actions on algebraic quantizations. Algebra Number Theory, 10(10):2287–2310, 2016. P. Etingof and C. Walton. Finite dimensional Hopf actions on deformation quantizations. Proc. Amer. Math. Soc., 145(5):1917–1925, 2016. E. Fontes, G. Martini, and G. Fonseca. Partial actions of weak Hopf algebras on coalgebras. J. Algebra Appl., 21(01):Paper No. 2250012, 35, oct 2020. G. Fonseca, G. Martini, and L. Silva. Partial (co)actions of Taft and Nichols Hopf algebras on their base fields. Int. J. Algebra Comput., 31(07):1471–1496, 2021. G. Fonseca, G. Martini, and L. Silva. Partial (co)actions of Taft and Nichols Hopf algebras on algebras. ArXiv preprint arXiv:math/2208.05141, 2022. R. Fröberg. Koszul algebras. In D. Dobbs, M. Fontana, and S. E. Kabbaj, editors, Advances in commutative ring theory, volume 205 of Lecture Notes in Pure and Applied Mathematics, pages 337–350. Marcel Dekker, 1999. K. R. Goodearl and R. B. Jr Warfield. An Introduction to Noncommutative Noetherian Rings, volume 61 of London Mathematical Society Student Texts. Cambridge University Press, second edition, 2004. T. Hayashi. Quantum group symmetry of partition functions of IRF models and its application to Jones’ index theory. Comm. Math. Phys., 157(2):331–345, 1993. T. Hayashi. Compact quantum groups of face type. Publ. Res. Inst. Math. Sci., 32(2):351–369, 1996. T. Hayashi. Face algebras and unitarity of SU(N)L-TQFT. Comm. Math. Phys., 203(1):211–247, 1999. H. Huang, C. Walton, E. Wicks, and R. Won. Universal quantum semigroupoids. J. Pure Appl. Algebra, 227:107193, 2023. A. Ibort and M. Rodríguez. An introduction to groups, groupoids and their representations. CRC Press, 2019. A. Ibort and M. Rodríguez. On the structure of finite groupoids and their representations. Symmetry, 11(3):414, 2019. L. Kong and I. Runkel. Cardy algebras and sewing constraints. I. Comm. Math. Phys., 292(3):871–912, 2009. K. Mackenzie. Lie Groupoids and Lie Algebroids in Differential Geometry, volume 124 of London Mathematical Society Lecture Note Series. Cambridge University Press, 1987. J. M. Moreno-Fernández and M. Siles-Molina. Graph algebras and the Gelfand-Kirillov dimension. J. Algebra Appl., 17(05):1850095, 15, 2018. S. Montgomery. Hopf Algebras and Their Actions on Rings, volume 82 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, 1993. G. Martini, A. Paques, and L. Duarte-Silva. Partial actions of a Hopf algebra on its base field and the corresponding partial smash product algebra. J. Algebra Appl., 22(06):2350140, 2022. J. C. McConnell and J. C. Robson. Noncommutative Noetherian rings, volume 30 of Graduate Studies in Mathematics. American Mathematical Society, 2001. D. Nikshych. Quantum groupoids, their representation categories, symmetries of von Neumann factors, and dynamical quantum groups. PhD thesis, University of California, 2001. D. Nikshych. On the structure of weak Hopf algebras. Adv. Math., 170(2):257–286, 2002. D. Nikshych. Semisimple weak Hopf algebras. J. Algebra, 275(2):639–667, 2004. F. Nill. Axioms for weak bialgebras. arXiv preprint arXiv:math/9805104, 1998. F. Nill, K. Szlachanyi, and H. W. Wiesbrock. Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers. arXiv preprint arXiv:math/9806130, 1998. D. Nikshych, V. Turaev, and L. Vainerman. Invariants of knots and 3-manifold from quantum groupoids. Topology Appl., 127(1-2):91–123, 2003. D. Nikshych and L. Vainerman. Finite quantum groupoids and their applications. In S. Montgomery and H. J. Schneider, editors, New directions in Hopf algebras, volume 43 of Mathematical Sciences Research Institute Publications, pages 211–262. Cambridge Univ. Press, Cambridge, 2002.I A. Paques and D. Flôres. Duality for groupoid (co)actions. Comm. Algebra, 42(2):637–663, 2013. H. Pfeiffer. Fusion categories in terms of graphs and relations. Quantum Topol., 2(4):339–379, 2011. J. Pradines. Théorie de lie pour les groupoïdes différentiables. Calcul différentiel dans la catégorie des groupoïdes infinitésimaux. C. R. Math. Acad. Sci. Paris, 264:A245–A248, 1967. A. Paques and T. Tamusiunas. A Galois-Grothendieck-type correspondence for groupoid actions. Algebra Discrete Math., 17(1):80–97, 2014. G. S. Rinehart. Differential forms on general commutative algebras. Trans. Amer. Math. Soc., 108(2):195–222, 1963. D. Rogalski, R. Won, and J. J. Zhang. A proof of the Brown-Goodearl conjecture for module-finite weak Hopf algebras. Algebra Number Theory, 15(4):971–997, 2021. Paolo Saracco. On anchored Lie algebras and the Connes-Moscovici’s bialgebroid construction. ArXiv preprint arXiv:math/2009.14656, 2020. Paolo Saracco. Universal enveloping algebras of Lie-Rinehart algebras as a left adjoint functor. ArXiv preprint arXiv:math/2102.01553, 2021. M. Siles-Molina. Algebras of quotients of path algebras. J. Algebra, 319(12):5265–5278, 2008. R. Street. Quantum Groups: a path to current algebra, volume 19 of Australian Mathematical Society Lecture Series. Cambridge University Press, 2007. I. Shestakov and U. Umirbaev. The tame and the wild automorphisms of polynomial rings in three variables. J. Amer. Math. Soc., 17(1):197–227, 2004. K. Szlachányi. Finite quantum groupoids and inclusions of finite type. In Mathematical physics in mathematics and physics (Siena, 2000), volume 30 of Fields Inst. Commun., pages 393–407. Amer. Math. Soc., Providence, RI, 2001. K. Szlachányi. Adjointable monoidal functors and quantum groupoids. In Hopf algebras in noncommutative geometry and physics, volume 239 of Lecture Notes in Pure and Appl. Math., pages 291–307. Dekker, New York, 2005. V. Ufnarovski˘ı. A growth criterion for graphs and algebras defined by words. Mat. Zametki, 31(3):465–472, 476, 1982. J. C. Várilly. Hopf algebras in noncommutative geometry. In A. Cardona, S. Paycha, and H. Ocampo, editors, Geometric and Topological Methods for Quantum Field Theory, pages 1–85. World Scientific, 2003. C. Walton and X. Wang. On quantum groups associated to non-Noetherian regular algebras of dimension 2. Math. Z., 284(1-2):543–574, 2016. C. Walton, E. Wicks, and R. Won. Algebraic structures in comodule categories over weak bialgebras. Comm. Algebra, 50(7):2877–2910, 2022.
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dc.format.extent.spa.fl_str_mv	vii, 79 páginas
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Doctorado en Ciencias - Matemáticas
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá,Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Chelsea, Walton5da809a83f6de007a75de24a5683ef00Milton Armando, Reyes Villamil7ca94419d65ec3833d498624271e6694Calderón Mateus, Fabio Alejandro4443ae4aa2f3c3a95fab4ffa11c4ba60600Calderón, Fabio [0000-0003-1777-0805]2023-07-31T19:42:30Z2023-07-31T19:42:30Z2023-07-24https://repositorio.unal.edu.co/handle/unal/84376Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)representations, and applications in groupoids, path algebras, and Lie algebroids. The research employs algebraic and categorical techniques to explore the foundational properties of these structures, establishing connections between algebraic and categorical frameworks, and addressing open problems related to their actions on noncommutative graded algebras. By combining theoretical findings and practical examples, this work enhances our understanding of weak Hopf algebras as symmetry generators and their broader implications in various mathematical contexts. Our results contribute to the field of noncommutative algebra and Hopf algebras, paving the way for future research in these areas. (Texto tomado de la fuente)Esta tesis investiga las propiedades de las biálgebras débiles (weak bialgebras) y las álgebras de Hopf débiles (weak Hopf algebras), sus (co)representaciones y aplicaciones en groupoides, álgebras de caminos y álgebroides de Lie. La investigación emplea técnicas algebraicas y categóricas para explorar las propiedades fundamentales de estas estructuras, estableciendo conexiones entre los marcos algebraicos y categóricos, y abordando problemas abiertos relacionados con sus acciones en álgebras graduadas no conmutativas. Combinando hallazgos teóricos y ejemplos prácticos, este trabajo mejora nuestra comprensión de las álgebras de Hopf débiles como generadores de simetrías y sus implicaciones más amplias en diversos contextos matemáticos. Nuestros resultados contribuyen al campo del álgebra no conmutativa y las álgebras de Hopf, allanando el camino para futuras investigaciones en estas áreas.DoctoradoDoctor en Ciencias - Matemáticasvii, 79 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - MatemáticasFacultad de CienciasBogotá,ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::512 - ÁlgebraFormas matemáticasForms (mathematics)Monoidal categoryWeak Hopf algebraRepresentation theoryGroupoidLie algebroidPath algebraQuiverÁlgebra de Hopf débilCategoría monoidalTeoría de representacionesGrupoideAlgebroide de LieÁlgebra de caminosCarcajAlgebraic properties of weak quantum symmetriesPropiedades algebraicas de las simetrías cuánticas débilesTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDM. Alves, E. Batista, and J. Vercruysse. Partial representations of hopf algebras. J. Algebra, 426:137–187, 2015.N. Andruskiewitsch, W. R. Ferrer-Santos, and H. J. Schneider, editors. New trends in Hopf algebra theory. Proceedings of the Colloquium on Quantum Groups and Hopf Algebras held in La Falda, August 9–13, 1999, volume 267 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 2000.I. Assem, A. Skowronski, and D. Simson. Elements of the representation theory of associative algebras. Vol. 1: Techniques of representation theory, volume 65 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2006.G. Böhm. Hopf Algebras and Their Generalizations from a Category Theoretical Point of View, volume 2226 of Lecture Notes in Mathematics. Springer International Publishing, 2018.Y. Bahturin. Identical Relations in Lie Algebras, volume 68 of De Gruyter Expositions in Mathematics. De Gruyter, sec edition, 2021. Translated from the Russian by Bahturin.G. Böhm, S. Caenepeel, and K. Janssen. Weak bialgebras and monoidal categories. Comm. Algebra, 39(12):4584–4607, 2011.M. Artin, W. Schelter, and J. Tate. Quantum deformations of GLn. Comm. Pure Appl. Math., 44(8-9):879–895, 1991T. Brzeziński, S. Caenepeel, and G. Militaru. Doi-Koppinen modules for quantum groupoids. J. Pure Appl. Algebra, 175(1-3):45–62, 2002. Special volume celebrating the 70th birthday of Professor Max Kelly.D. Bagio, D. Florez, and A. Paques. Partial actions of ordered groupoids on rings. J. Algebra Appl., 09(3):501–517, 2010.K. A. Brown and K. R. Goodearl. Lectures on Algebraic Quantum Groups. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser Basel, 2002.G. Böhm, J. Gómez-Torrecillas, and E. López-Centella. On the category of weak bialgebras. J. Algebra, 399:801–844, 2014.R. Brown, P. J. Higgins, and R. Sivera. Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids. Number 15 in Tracts in Mathematics. EMS Press, 2011.G. Bôhm, F. Nill, and K. Szlachányi. Weak Hopf algebras. I. Integral theory and C-structure. J. Algebra, 221(2):385–438, 1999.D. Bagio and A. Paques. Partial groupoid actions: Globalization, Morita theory, and Galois theory. Comm. Algebra, 40(10):3658–3678, 2012.M. Brion. Representations of quivers. In Geometric methods in representation theory (I), volume 24 of Séminaires & Congrès: Collection SMF, pages 103–144. Société Mathématique de France, 2012J. Cuadra, P. Etingof, and C. Walton. Semisimple Hopf actions on Weyl algebras. Adv. Math., 282:47–55, 2015.J. Cuadra, P. Etingof, and C. Walton. Finite dimensional Hopf actions on Weyl algebras. Adv. Math., 302:25–39, 2016.S. Caenepeel and E. De Groot. Modules over weak entwining structures. In N. Andruskiewitsch, W. R. Ferrer-Santos, and H. J. Schneider, editors, New trends in Hopf algebra theory. Proceedings of the Colloquium on Quantum Groups and Hopf Algebras held in La Falda, August 9–13, 1999, volume 267 of Contemp. Math., pages 31–54. Amer. Math. Soc., Providence, RI, 2000.F. Calderón, H. Huang, E. Wicks, and R. Won. Symmetries captured by actions of weak Hopf algebras. arXiv preprint arXiv:2209.11903, 2023.K. Chan, E. Kirkman, C. Walton, and J. J. Zhang. Quantum binary polyhedral groups and their actions on quantum planes. J. Reine Angew. Math., 719:211–252, 2016.F. U. Coelho and S. X. Liu. Generalized path algebras. In F. van Oystaeyen and M. Saorin, editors, Interactions between ring theory and representations of algebras, volume 210 of Lecture Notes in Pure and Applied Mathematics, pages 53–66. CRC, 2000.D. Cheng and F. Li. The structure of weak Hopf algebras corresponding to Uq(sl2). Comm. Algebra, 37(3):729–742, 2009.G. Böhm and K. Szlachányi. Weak C-Hopf algebras: the coassociative symmetry of non-integral dimensions. In R. Budzyński, W. Pusz, and S. Zakrzewski, editors, Quantum groups and quantum spaces (Warsaw, 1995), volume 40 of Banach Center Publ., pages 9–19. Polish Acad. Sci. Inst. Math., Warsaw, 1997.M. Cohen and S. Montgomery. Group-graded rings, smash products, and group actions. Trans. Amer. Math. Soc., 282(1):237–258, 1984.F. Castro, A. Paques, G. Quadros, and A. Sant’Ana. Partial actions of weak Hopf algebras: Smash product, globalization and Morita theory. J. Pure Appl. Algebra, 219(12):5511–5538, 2015.F. Calderón and A. Reyes. On the (partial) representation category of weak Hopf algebras. In preparation, 2023.F. Calderón and C. Walton. Algebraic properties of face algebras. J. Algebra Appl., 22(03):2350076, 2023.S. Dăscălescu, C. Năstăsescu, and Ş. Raianu. Hopf Algebras: An Introduction, volume 235 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., first edition, 2001.M. Dokuchaev. Recent developments around partial actions. São Paulo J. Math. Sci., 13(1):195–247, 2018.B. Day and C. Pastro. Note on Frobenius monoidal functors. New York J. Math., 14:733–742, 2008.P. Etingof and C. H. Eu. 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Algebra, 50(7):2877–2910, 2022.EstudiantesInvestigadoresORIGINAL_FC__Doctoral_Dissertation.pdf_FC__Doctoral_Dissertation.pdfTesis de Doctorado en Ciencias - Matemáticasapplication/pdf872867https://repositorio.unal.edu.co/bitstream/unal/84376/2/_FC__Doctoral_Dissertation.pdf532cf8a13ce1eb4b48959a1aabec00faMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84376/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51THUMBNAIL_FC__Doctoral_Dissertation.pdf.jpg_FC__Doctoral_Dissertation.pdf.jpgGenerated Thumbnailimage/jpeg4140https://repositorio.unal.edu.co/bitstream/unal/84376/3/_FC__Doctoral_Dissertation.pdf.jpg9e916296ba2a63189c0e35eefaa43e31MD53unal/84376oai:repositorio.unal.edu.co:unal/843762024-08-17 00:01:33.426Repositorio Institucional Universidad Nacional de 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Algebraic properties of weak quantum symmetries

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