Algunas propiedades homológicas del plano de Jordan
1 recurso en línea (páginas 69-82).
- Autores:
-
Gómez Parada, Jonatan Andrés
Suárez Suárez, Héctor Julio
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2018
- Institución:
- Universidad Pedagógica y Tecnológica de Colombia
- Repositorio:
- RiUPTC: Repositorio Institucional UPTC
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.uptc.edu.co:001/2369
- Acceso en línea:
- http://repositorio.uptc.edu.co/handle/001/2369
- Palabra clave:
- Plano de Jordan
Algebras Artin-Schelter regulares
Algebras Calabi-Yau torcidas
Automorfismo de Nakayama
- Rights
- openAccess
- License
- Copyright (c) 2018 Universidad Pedagógica y Tecnológica de Colombia
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Algunas propiedades homológicas del plano de Jordan |
| dc.title.alternative.eng.fl_str_mv |
Some homological properties of Jordan plane |
| title |
Algunas propiedades homológicas del plano de Jordan |
| spellingShingle |
Algunas propiedades homológicas del plano de Jordan Plano de Jordan Algebras Artin-Schelter regulares Algebras Calabi-Yau torcidas Automorfismo de Nakayama |
| title_short |
Algunas propiedades homológicas del plano de Jordan |
| title_full |
Algunas propiedades homológicas del plano de Jordan |
| title_fullStr |
Algunas propiedades homológicas del plano de Jordan |
| title_full_unstemmed |
Algunas propiedades homológicas del plano de Jordan |
| title_sort |
Algunas propiedades homológicas del plano de Jordan |
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Gómez Parada, Jonatan Andrés Suárez Suárez, Héctor Julio |
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Gómez Parada, Jonatan Andrés Suárez Suárez, Héctor Julio |
| dc.subject.proposal.spa.fl_str_mv |
Plano de Jordan Algebras Artin-Schelter regulares Algebras Calabi-Yau torcidas Automorfismo de Nakayama |
| topic |
Plano de Jordan Algebras Artin-Schelter regulares Algebras Calabi-Yau torcidas Automorfismo de Nakayama |
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1 recurso en línea (páginas 69-82). |
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2018 |
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2018-07-04 |
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2019-01-31T20:47:50Z |
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2019-01-31T20:47:50Z |
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Suárez Suárez, H. J. & Gómez Parada, J. A. (2018). Algunas propiedades homológicas del plano de Jordan. Ciencia en Desarrollo, 9(2), 69-82. DOI: https://doi.org/10.19053/01217488.v9.n2.2018.8140. http://repositorio.uptc.edu.co/handle/001/2369 |
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Suárez Suárez, H. J. & Gómez Parada, J. A. (2018). Algunas propiedades homológicas del plano de Jordan. Ciencia en Desarrollo, 9(2), 69-82. DOI: https://doi.org/10.19053/01217488.v9.n2.2018.8140. http://repositorio.uptc.edu.co/handle/001/2369 2462-7658 10.19053/01217488.v9.n2.2018.8140 |
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N. Andruskiewitsch, I. Angiono, I. Heckenberger, “Liftings of Jordan and Super Jordan Planes”, Proc. Edinb. Math. Soc., vol. 61, no. 3, pp. 661-672, 2018. N. Andruskiewitsch, I. Angiono, I. Heckenberger, “On finite GK-dimensional Nichols algebras over abelian groups”, arXiv:1606.02521v2 [math.QA], 2018. N. Andruskiewitsch, D. Bagio, S. Della Flora y D. Flôres, “Representations of the super Jordan plane”, São Paulo J. Math. Sci., vol. 11, no. 2, pp. 312-325, 2017 M. Artin y W. Schelter, “Graded Algebras of Global Dimension 3”, Adv. Math., vol. 66, pp. 171-206, 1987. E. E. Demidov, Yu. I. Manin, E. E. Mukhin and D. V. Zhdanovich, “Nonstandard quantum deformations of GL(n) and constant solutions of the Yang-Baxter equation”, Common trends in mathematics and quantum field theories (Kyo-to, 1990). Progr. Theoret. Phys. Suppl., no. 102 (1990), pp. 203-218 (1991). C. Gallego y O. Lezama, “Gröbner bases for ideals of σ−PBW extensions”, Comm. Algebra, vol. 39, pp. 50-75, 2011. V. Ginzburg, “Calabi-Yau algebras”, arXiv:math.AG/0612139v3, vol. 51, pp. 329-333, 2006. N. R. González y Y. P. Suárez, "Ideales en el Anillo de Polinomios Torcidos R[x;σ,δ]", Ciencia en Desarrollo, vol. 5, no. 1, pp. 31- 37, 2014. J. Goodman y U. Krähmer, “Untwisting a twisted Calabi-Yau algebra”, J. Algebra, vol. 406, pp. 272-289, 2014 D. I. Gurevich, “The Yang-Baxter equation and the generalization of formal Lie theory”, Dokl. Akad. Nauk SSSR, vol. 288, no. 4, pp. 797-801, 1986. J.W He, F. Oystaeyen y Y. Zhang, “Calabi-Yau algebras and their deformations”, Bull. Math. Soc. Sci. Math. Roumanie, vol. 56, no. 3, pp. 335- 347, 2013. N. Iyudu, “Representation Spaces of the Jordan Plane”, Comm. Algebra, vol. 42, no. 8, pp. 3507-3540, 2014. S. Korenskii, “Representations of the Quantum group SLj(2)”, Rus. Math. Surv, vol. 46, no. 6, pp. 211-212, 1991. G. R. Krause y T. H. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Grad. Stud. Math., 22, AMS (2000). J. McConnell y J. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, AMS (2001). O. Lezama y E. Latorre, “Noncommutative algebraic geometry of semigraded rings”, Internat. J. Algebra Comput., vol. 27, no. 4, pp. 361-389, 2017. L. Liu, S. Wang y Q. Wu, “Twisted Calabi-Yau property of Ore extensions”, J. Noncommut. Geom., vol. 8, no. 2, pp. 587-609, 2014. S. Reca y A. Solotar 2018. “Homological invariants relating the super Jordan plane to the Virasoro algebra”, J. Algebra, vol. 507, pp. 120-185. A. Reyes y H. Suárez, “Some remarks about the cyclic homology of skew PBW extensions", Ciencia en Desarrollo, vol. 7, no. 2, pp. 99-107, 2016. M. Reyes, D. Rogalski y J. J Zhang, “Skew Calabi-Yau algebras and homological identi-ties”, Adv. Math., vol. 264, pp. 308 -354, 2014. D. Rogalski, “An introduction to non-commutative projective algebraic geometry”, arXiv:1403.3065 [math.RA], 2014. H. Suárez, “Koszulity for graded skew PBW extensions”, Comm. Algebra, vol. 45, no. 10, pp. 4569-4580, 2017. H. Suárez, O. Lezama y A. Reyes, “Some Relations between N-Koszul, Artin-Schelter Regular and Calabi-Yau with Skew PBW Extensions”, Ciencia en Desarrollo, vol. 6, no. 2, pp. 205- 213, 2015. H. Suárez, O. Lezama y A. Reyes, “Calabi-Yau property for graded skew PBW extensions”, Rev. Colombiana Mat., vol. 51, no. 2, pp. 221-238, 2017. H. Suárez y A. Reyes, “Koszulity for skew PBW extension over fields”, JP J. Algebra Number Theory Appl., vol. 39, no. 2, pp. 181-203, 2017. |
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Ciencia en Desarrollo;Volumen 9, número 2 (Julio-Diciembre 2018) |
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Copyright (c) 2018 Universidad Pedagógica y Tecnológica de Colombia |
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Gómez Parada, Jonatan AndrésSuárez Suárez, Héctor Julio2019-01-31T20:47:50Z2019-01-31T20:47:50Z2018-07-04Suárez Suárez, H. J. & Gómez Parada, J. A. (2018). Algunas propiedades homológicas del plano de Jordan. Ciencia en Desarrollo, 9(2), 69-82. DOI: https://doi.org/10.19053/01217488.v9.n2.2018.8140. http://repositorio.uptc.edu.co/handle/001/23692462-7658http://repositorio.uptc.edu.co/handle/001/236910.19053/01217488.v9.n2.2018.81401 recurso en línea (páginas 69-82).The Jordan plane can be seen as a quotient algebra, as a graded Ore extension and as a graded skew PBW extension. Using these interpretations, it is proved that the Jordan plane is an Artin-Schelter regular algebra and a skew Calabi-Yau algebra, in addition its Nakayama automorphism is explicitly calculated.El plano de Jordan puede ser visto como un álgebra cociente, como una extensión de Ore graduada y como una extensión PBW torcida graduada. Usando estas interpretaciones, se muestra que el plano de Jordan es un álgebra Artin-Schelter regular y Calabi-Yau torcida, además se calcula de forma explícita su automorfismo de Nakayama.Bibliografía: páginas 81-82.application/pdfspaUniversidad Pedagógica y Tecnológica de ColombiaCopyright (c) 2018 Universidad Pedagógica y Tecnológica de Colombiahttps://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)http://purl.org/coar/access_right/c_abf2https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8140/7259Algunas propiedades homológicas del plano de JordanSome homological properties of Jordan planeArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTexthttps://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85N. Andruskiewitsch, I. Angiono, I. Heckenberger, “Liftings of Jordan and Super Jordan Planes”, Proc. Edinb. Math. Soc., vol. 61, no. 3, pp. 661-672, 2018.N. Andruskiewitsch, I. Angiono, I. Heckenberger, “On finite GK-dimensional Nichols algebras over abelian groups”, arXiv:1606.02521v2 [math.QA], 2018.N. Andruskiewitsch, D. Bagio, S. Della Flora y D. Flôres, “Representations of the super Jordan plane”, São Paulo J. Math. Sci., vol. 11, no. 2, pp. 312-325, 2017M. Artin y W. Schelter, “Graded Algebras of Global Dimension 3”, Adv. Math., vol. 66, pp. 171-206, 1987.E. E. Demidov, Yu. I. Manin, E. E. Mukhin and D. V. Zhdanovich, “Nonstandard quantum deformations of GL(n) and constant solutions of the Yang-Baxter equation”, Common trends in mathematics and quantum field theories (Kyo-to, 1990). Progr. Theoret. Phys. Suppl., no. 102 (1990), pp. 203-218 (1991).C. Gallego y O. Lezama, “Gröbner bases for ideals of σ−PBW extensions”, Comm. Algebra, vol. 39, pp. 50-75, 2011.V. Ginzburg, “Calabi-Yau algebras”, arXiv:math.AG/0612139v3, vol. 51, pp. 329-333, 2006.N. R. González y Y. P. Suárez, "Ideales en el Anillo de Polinomios Torcidos R[x;σ,δ]", Ciencia en Desarrollo, vol. 5, no. 1, pp. 31- 37, 2014.J. Goodman y U. Krähmer, “Untwisting a twisted Calabi-Yau algebra”, J. Algebra, vol. 406, pp. 272-289, 2014D. I. Gurevich, “The Yang-Baxter equation and the generalization of formal Lie theory”, Dokl. Akad. Nauk SSSR, vol. 288, no. 4, pp. 797-801, 1986.J.W He, F. Oystaeyen y Y. Zhang, “Calabi-Yau algebras and their deformations”, Bull. Math. Soc. Sci. Math. Roumanie, vol. 56, no. 3, pp. 335- 347, 2013.N. Iyudu, “Representation Spaces of the Jordan Plane”, Comm. Algebra, vol. 42, no. 8, pp. 3507-3540, 2014.S. Korenskii, “Representations of the Quantum group SLj(2)”, Rus. Math. Surv, vol. 46, no. 6, pp. 211-212, 1991.G. R. Krause y T. H. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Grad. Stud. Math., 22, AMS (2000).J. McConnell y J. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, AMS (2001).O. Lezama y E. Latorre, “Noncommutative algebraic geometry of semigraded rings”, Internat. J. Algebra Comput., vol. 27, no. 4, pp. 361-389, 2017.L. Liu, S. Wang y Q. Wu, “Twisted Calabi-Yau property of Ore extensions”, J. Noncommut. Geom., vol. 8, no. 2, pp. 587-609, 2014.S. Reca y A. Solotar 2018. “Homological invariants relating the super Jordan plane to the Virasoro algebra”, J. Algebra, vol. 507, pp. 120-185.A. Reyes y H. Suárez, “Some remarks about the cyclic homology of skew PBW extensions", Ciencia en Desarrollo, vol. 7, no. 2, pp. 99-107, 2016.M. Reyes, D. Rogalski y J. J Zhang, “Skew Calabi-Yau algebras and homological identi-ties”, Adv. Math., vol. 264, pp. 308 -354, 2014.D. Rogalski, “An introduction to non-commutative projective algebraic geometry”, arXiv:1403.3065 [math.RA], 2014.H. Suárez, “Koszulity for graded skew PBW extensions”, Comm. Algebra, vol. 45, no. 10, pp. 4569-4580, 2017.H. Suárez, O. Lezama y A. Reyes, “Some Relations between N-Koszul, Artin-Schelter Regular and Calabi-Yau with Skew PBW Extensions”, Ciencia en Desarrollo, vol. 6, no. 2, pp. 205- 213, 2015.H. Suárez, O. Lezama y A. Reyes, “Calabi-Yau property for graded skew PBW extensions”, Rev. Colombiana Mat., vol. 51, no. 2, pp. 221-238, 2017.H. Suárez y A. Reyes, “Koszulity for skew PBW extension over fields”, JP J. Algebra Number Theory Appl., vol. 39, no. 2, pp. 181-203, 2017.Ciencia en Desarrollo;Volumen 9, número 2 (Julio-Diciembre 2018)Plano de JordanAlgebras Artin-Schelter regularesAlgebras Calabi-Yau torcidasAutomorfismo de NakayamaORIGINALPPS_964_Algunas_propiedades_homologicas.pdfPPS_964_Algunas_propiedades_homologicas.pdfArchivo principalapplication/pdf1409210https://repositorio.uptc.edu.co/bitstreams/b50e9076-4a20-420e-849d-9828c10ae2aa/download62ec6fa955156ae8804273aacaad3ed7MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-814798https://repositorio.uptc.edu.co/bitstreams/9778a0e8-0ede-4a8f-8624-7c6f8c88beac/download88794144ff048353b359a3174871b0d5MD52TEXTPPS-964.pdf.txtPPS-964.pdf.txtExtracted texttext/plain30967https://repositorio.uptc.edu.co/bitstreams/7ef11703-0254-4a98-93dc-970dae8f4e5f/download9fbfb38a75bb3d189cae6488e1e44bf9MD53PPS_964_Algunas_propiedades_homologicas.pdf.txtPPS_964_Algunas_propiedades_homologicas.pdf.txtExtracted 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BlbCBub21icmUgZGUgbGEgcGFydGUgbyBsYXMgcGFydGVzIHF1ZSBlbCBBdXRvciBPcmlnaW5hbCB5L28gZWwgTGljZW5jaWFudGUgaHViaWVyZW4gZGVzaWduYWRvIHBhcmEgbGEgYXRyaWJ1Y2nDs24gKHYuZy4sIHVuIGluc3RpdHV0byBwYXRyb2NpbmFkb3IsIGVkaXRvcmlhbCwgcHVibGljYWNpw7NuKSBlbiBsYSBpbmZvcm1hY2nDs24gZGUgbG9zIGRlcmVjaG9zIGRlIGF1dG9yIGRlbCBMaWNlbmNpYW50ZSwgdMOpcm1pbm9zIGRlIHNlcnZpY2lvcyBvIGRlIG90cmFzIGZvcm1hcyByYXpvbmFibGVzOyBlbCB0w610dWxvIGRlIGxhIE9icmEgc2kgZXN0w6EgcHJvdmlzdG87IGVuIGxhIG1lZGlkYSBkZSBsbyByYXpvbmFibGVtZW50ZSBmYWN0aWJsZSB5LCBzaSBlc3TDoSBwcm92aXN0bywgZWwgSWRlbnRpZmljYWRvciBVbmlmb3JtZSBkZSBSZWN1cnNvcyAoVW5pZm9ybSBSZXNvdXJjZSBJZGVudGlmaWVyKSBxdWUgZWwgTGljZW5jaWFudGUgZXNwZWNpZmljYSBwYXJhIHNlciBhc29jaWFkbyBjb24gbGEgT2JyYSwgc2Fsdm8gcXVlIHRhbCBVUkkgbm8gc2UgcmVmaWVyYSBhIGxhIG5vdGEgc29icmUgbG9zIGRlcmVjaG9zIGRlIGF1dG9yIG8gYSBsYSBpbmZvcm1hY2nDs24gc29icmUgZWwgbGljZW5jaWFtaWVudG8gZGUgbGEgT2JyYTsgeSBlbiBlbCBjYXNvIGRlIHVuYSBPYnJhIERlcml2YWRhLCBhdHJpYnVpciBlbCBjcsOpZGl0byBpZGVudGlmaWNhbmRvIGVsIHVzbyBkZSBsYSBPYnJhIGVuIGxhIE9icmEgRGVyaXZhZGEgKHYuZy4sICJUcmFkdWNjacOzbiBGcmFuY2VzYSBkZSBsYSBPYnJhIGRlbCBBdXRvciBPcmlnaW5hbCwiIG8gIkd1acOzbiBDaW5lbWF0b2dyw6FmaWNvIGJhc2FkbyBlbiBsYSBPYnJhIG9yaWdpbmFsIGRlbCBBdXRvciBPcmlnaW5hbCIpLiBUYWwgY3LDqWRpdG8gcHVlZGUgc2VyIGltcGxlbWVudGFkbyBkZSBjdWFscXVpZXIgZm9ybWEgcmF6b25hYmxlOyBlbiBlbCBjYXNvLCBzaW4gZW1iYXJnbywgZGUgT2JyYXMgRGVyaXZhZGFzIHUgT2JyYXMgQ29sZWN0aXZhcywgdGFsIGNyw6lkaXRvIGFwYXJlY2Vyw6EsIGNvbW8gbcOtbmltbywgZG9uZGUgYXBhcmVjZSBlbCBjcsOpZGl0byBkZSBjdWFscXVpZXIgb3RybyBhdXRvciBjb21wYXJhYmxlIHkgZGUgdW5hIG1hbmVyYSwgYWwgbWVub3MsIHRhbiBkZXN0YWNhZGEgY29tbyBlbCBjcsOpZGl0byBkZSBvdHJvIGF1dG9yIGNvbXBhcmFibGUuCmQuCVBhcmEgZXZpdGFyIHRvZGEgY29uZnVzacOzbiwgZWwgTGljZW5jaWFudGUgYWNsYXJhIHF1ZSwgY3VhbmRvIGxhIG9icmEgZXMgdW5hIGNvbXBvc2ljacOzbiBtdXNpY2FsOgppLglSZWdhbMOtYXMgcG9yIGludGVycHJldGFjacOzbiB5IGVqZWN1Y2nDs24gYmFqbyBsaWNlbmNpYXMgZ2VuZXJhbGVzLiBFbCBMaWNlbmNpYW50ZSBzZSByZXNlcnZhIGVsIGRlcmVjaG8gZXhjbHVzaXZvIGRlIGF1dG9yaXphciBsYSBlamVjdWNpw7NuIHDDumJsaWNhIG8gbGEgZWplY3VjacOzbiBww7pibGljYSBkaWdpdGFsIGRlIGxhIG9icmEgeSBkZSByZWNvbGVjdGFyLCBzZWEgaW5kaXZpZHVhbG1lbnRlIG8gYSB0cmF2w6lzIGRlIHVuYSBzb2NpZWRhZCBkZSBnZXN0acOzbiBjb2xlY3RpdmEgZGUgZGVyZWNob3MgZGUgYXV0b3IgeSBkZXJlY2hvcyBjb25leG9zIChwb3IgZWplbXBsbywgU0FZQ08pLCBsYXMgcmVnYWzDrWFzIHBvciBsYSBlamVjdWNpw7NuIHDDumJsaWNhIG8gcG9yIGxhIGVqZWN1Y2nDs24gcMO6YmxpY2EgZGlnaXRhbCBkZSBsYSBvYnJhIChwb3IgZWplbXBsbyBXZWJjYXN0KSBsaWNlbmNpYWRhIGJham8gbGljZW5jaWFzIGdlbmVyYWxlcywgc2kgbGEgaW50ZXJwcmV0YWNpw7NuIG8gZWplY3VjacOzbiBkZSBsYSBvYnJhIGVzdMOhIHByaW1vcmRpYWxtZW50ZSBvcmllbnRhZGEgcG9yIG8gZGlyaWdpZGEgYSBsYSBvYnRlbmNpw7NuIGRlIHVuYSB2ZW50YWphIGNvbWVyY2lhbCBvIHVuYSBjb21wZW5zYWNpw7NuIG1vbmV0YXJpYSBwcml2YWRhLgppaS4JUmVnYWzDrWFzIHBvciBGb25vZ3JhbWFzLiBFbCBMaWNlbmNpYW50ZSBzZSByZXNlcnZhIGVsIGRlcmVjaG8gZXhjbHVzaXZvIGRlIHJlY29sZWN0YXIsIGluZGl2aWR1YWxtZW50ZSBvIGEgdHJhdsOpcyBkZSB1bmEgc29jaWVkYWQgZGUgZ2VzdGnDs24gY29sZWN0aXZhIGRlIGRlcmVjaG9zIGRlIGF1dG9yIHkgZGVyZWNob3MgY29uZXhvcyAocG9yIGVqZW1wbG8sIGxvcyBjb25zYWdyYWRvcyBwb3IgbGEgU0FZQ08pLCB1bmEgYWdlbmNpYSBkZSBkZXJlY2hvcyBtdXNpY2FsZXMgbyBhbGfDum4gYWdlbnRlIGRlc2lnbmFkbywgbGFzIHJlZ2Fsw61hcyBwb3IgY3VhbHF1aWVyIGZvbm9ncmFtYSBxdWUgVXN0ZWQgY3JlZSBhIHBhcnRpciBkZSBsYSBvYnJhICjigJx2ZXJzacOzbiBjb3ZlcuKAnSkgeSBkaXN0cmlidXlhLCBlbiBsb3MgdMOpcm1pbm9zIGRlbCByw6lnaW1lbiBkZSBkZXJlY2hvcyBkZSBhdXRvciwgc2kgbGEgY3JlYWNpw7NuIG8gZGlzdHJpYnVjacOzbiBkZSBlc2EgdmVyc2nDs24gY292ZXIgZXN0w6EgcHJpbW9yZGlhbG1lbnRlIGRlc3RpbmFkYSBvIGRpcmlnaWRhIGEgb2J0ZW5lciB1bmEgdmVudGFqYSBjb21lcmNpYWwgbyB1bmEgY29tcGVuc2FjacOzbiBtb25ldGFyaWEgcHJpdmFkYS4KZS4JR2VzdGnDs24gZGUgRGVyZWNob3MgZGUgQXV0b3Igc29icmUgSW50ZXJwcmV0YWNpb25lcyB5IEVqZWN1Y2lvbmVzIERpZ2l0YWxlcyAoV2ViQ2FzdGluZykuIFBhcmEgZXZpdGFyIHRvZGEgY29uZnVzacOzbiwgZWwgTGljZW5jaWFudGUgYWNsYXJhIHF1ZSwgY3VhbmRvIGxhIG9icmEgc2VhIHVuIGZvbm9ncmFtYSwgZWwgTGljZW5jaWFudGUgc2UgcmVzZXJ2YSBlbCBkZXJlY2hvIGV4Y2x1c2l2byBkZSBhdXRvcml6YXIgbGEgZWplY3VjacOzbiBww7pibGljYSBkaWdpdGFsIGRlIGxhIG9icmEgKHBvciBlamVtcGxvLCB3ZWJjYXN0KSB5IGRlIHJlY29sZWN0YXIsIGluZGl2aWR1YWxtZW50ZSBvIGEgdHJhdsOpcyBkZSB1bmEgc29jaWVkYWQgZGUgZ2VzdGnDs24gY29sZWN0aXZhIGRlIGRlcmVjaG9zIGRlIGF1dG9yIHkgZGVyZWNob3MgY29uZXhvcyAocG9yIGVqZW1wbG8sIEFDSU5QUk8pLCBsYXMgcmVnYWzDrWFzIHBvciBsYSBlamVjdWNpw7NuIHDDumJsaWNhIGRpZ2l0YWwgZGUgbGEgb2JyYSAocG9yIGVqZW1wbG8sIHdlYmNhc3QpLCBzdWpldGEgYSBsYXMgZGlzcG9zaWNpb25lcyBhcGxpY2FibGVzIGRlbCByw6lnaW1lbiBkZSBEZXJlY2hvIGRlIEF1dG9yLCBzaSBlc3RhIGVqZWN1Y2nDs24gcMO6YmxpY2EgZGlnaXRhbCBlc3TDoSBwcmltb3JkaWFsbWVudGUgZGlyaWdpZGEgYSBvYnRlbmVyIHVuYSB2ZW50YWphIGNvbWVyY2lhbCBvIHVuYSBjb21wZW5zYWNpw7NuIG1vbmV0YXJpYSBwcml2YWRhLgo1LiBSZXByZXNlbnRhY2lvbmVzLCBHYXJhbnTDrWFzIHkgTGltaXRhY2lvbmVzIGRlIFJlc3BvbnNhYmlsaWRhZC4KQSBNRU5PUyBRVUUgTEFTIFBBUlRFUyBMTyBBQ09SREFSQU4gREUgT1RSQSBGT1JNQSBQT1IgRVNDUklUTywgRUwgTElDRU5DSUFOVEUgT0ZSRUNFIExBIE9CUkEgKEVOIEVMIEVTVEFETyBFTiBFTCBRVUUgU0UgRU5DVUVOVFJBKSDigJxUQUwgQ1VBTOKAnSwgU0lOIEJSSU5EQVIgR0FSQU5Uw41BUyBERSBDTEFTRSBBTEdVTkEgUkVTUEVDVE8gREUgTEEgT0JSQSwgWUEgU0VBIEVYUFJFU0EsIElNUEzDjUNJVEEsIExFR0FMIE8gQ1VBTFFVSUVSQSBPVFJBLCBJTkNMVVlFTkRPLCBTSU4gTElNSVRBUlNFIEEgRUxMQVMsIEdBUkFOVMONQVMgREUgVElUVUxBUklEQUQsIENPTUVSQ0lBQklMSURBRCwgQURBUFRBQklMSURBRCBPIEFERUNVQUNJw5NOIEEgUFJPUMOTU0lUTyBERVRFUk1JTkFETywgQVVTRU5DSUEgREUgSU5GUkFDQ0nDk04sIERFIEFVU0VOQ0lBIERFIERFRkVDVE9TIExBVEVOVEVTIE8gREUgT1RSTyBUSVBPLCBPIExBIFBSRVNFTkNJQSBPIEFVU0VOQ0lBIERFIEVSUk9SRVMsIFNFQU4gTyBOTyBERVNDVUJSSUJMRVMgKFBVRURBTiBPIE5PIFNFUiBFU1RPUyBERVNDVUJJRVJUT1MpLiBBTEdVTkFTIEpVUklTRElDQ0lPTkVTIE5PIFBFUk1JVEVOIExBIEVYQ0xVU0nDk04gREUgR0FSQU5Uw41BUyBJTVBMw41DSVRBUywgRU4gQ1VZTyBDQVNPIEVTVEEgRVhDTFVTScOTTiBQVUVERSBOTyBBUExJQ0FSU0UgQSBVU1RFRC4KNi4gTGltaXRhY2nDs24gZGUgcmVzcG9uc2FiaWxpZGFkLgpBIE1FTk9TIFFVRSBMTyBFWElKQSBFWFBSRVNBTUVOVEUgTEEgTEVZIEFQTElDQUJMRSwgRUwgTElDRU5DSUFOVEUgTk8gU0VSw4EgUkVTUE9OU0FCTEUgQU5URSBVU1RFRCBQT1IgREHDkU8gQUxHVU5PLCBTRUEgUE9SIFJFU1BPTlNBQklMSURBRCBFWFRSQUNPTlRSQUNUVUFMLCBQUkVDT05UUkFDVFVBTCBPIENPTlRSQUNUVUFMLCBPQkpFVElWQSBPIFNVQkpFVElWQSwgU0UgVFJBVEUgREUgREHDkU9TIE1PUkFMRVMgTyBQQVRSSU1PTklBTEVTLCBESVJFQ1RPUyBPIElORElSRUNUT1MsIFBSRVZJU1RPUyBPIElNUFJFVklTVE9TIFBST0RVQ0lET1MgUE9SIEVMIFVTTyBERSBFU1RBIExJQ0VOQ0lBIE8gREUgTEEgT0JSQSwgQVVOIENVQU5ETyBFTCBMSUNFTkNJQU5URSBIQVlBIFNJRE8gQURWRVJUSURPIERFIExBIFBPU0lCSUxJREFEIERFIERJQ0hPUyBEQcORT1MuIEFMR1VOQVMgTEVZRVMgTk8gUEVSTUlURU4gTEEgRVhDTFVTScOTTiBERSBDSUVSVEEgUkVTUE9OU0FCSUxJREFELCBFTiBDVVlPIENBU08gRVNUQSBFWENMVVNJw5NOIFBVRURFIE5PIEFQTElDQVJTRSBBIFVTVEVELgo3LiBUw6lybWluby4KYS4JRXN0YSBMaWNlbmNpYSB5IGxvcyBkZXJlY2hvcyBvdG9yZ2Fkb3MgZW4gdmlydHVkIGRlIGVsbGEgdGVybWluYXLDoW4gYXV0b23DoXRpY2FtZW50ZSBzaSBVc3RlZCBpbmZyaW5nZSBhbGd1bmEgY29uZGljacOzbiBlc3RhYmxlY2lkYSBlbiBlbGxhLiBTaW4gZW1iYXJnbywgbG9zIGluZGl2aWR1b3MgbyBlbnRpZGFkZXMgcXVlIGhhbiByZWNpYmlkbyBPYnJhcyBEZXJpdmFkYXMgbyBDb2xlY3RpdmFzIGRlIFVzdGVkIGRlIGNvbmZvcm1pZGFkIGNvbiBlc3RhIExpY2VuY2lhLCBubyB2ZXLDoW4gdGVybWluYWRhcyBzdXMgbGljZW5jaWFzLCBzaWVtcHJlIHF1ZSBlc3RvcyBpbmRpdmlkdW9zIG8gZW50aWRhZGVzIHNpZ2FuIGN1bXBsaWVuZG8gw61udGVncmFtZW50ZSBsYXMgY29uZGljaW9uZXMgZGUgZXN0YXMgbGljZW5jaWFzLiBMYXMgU2VjY2lvbmVzIDEsIDIsIDUsIDYsIDcsIHkgOCBzdWJzaXN0aXLDoW4gYSBjdWFscXVpZXIgdGVybWluYWNpw7NuIGRlIGVzdGEgTGljZW5jaWEuCmIuCVN1amV0YSBhIGxhcyBjb25kaWNpb25lcyB5IHTDqXJtaW5vcyBhbnRlcmlvcmVzLCBsYSBsaWNlbmNpYSBvdG9yZ2FkYSBhcXXDrSBlcyBwZXJwZXR1YSAoZHVyYW50ZSBlbCBwZXLDrW9kbyBkZSB2aWdlbmNpYSBkZSBsb3MgZGVyZWNob3MgZGUgYXV0b3IgZGUgbGEgb2JyYSkuIE5vIG9ic3RhbnRlIGxvIGFudGVyaW9yLCBlbCBMaWNlbmNpYW50ZSBzZSByZXNlcnZhIGVsIGRlcmVjaG8gYSBwdWJsaWNhciB5L28gZXN0cmVuYXIgbGEgT2JyYSBiYWpvIGNvbmRpY2lvbmVzIGRlIGxpY2VuY2lhIGRpZmVyZW50ZXMgbyBhIGRlamFyIGRlIGRpc3RyaWJ1aXJsYSBlbiBsb3MgdMOpcm1pbm9zIGRlIGVzdGEgTGljZW5jaWEgZW4gY3VhbHF1aWVyIG1vbWVudG87IGVuIGVsIGVudGVuZGlkbywgc2luIGVtYmFyZ28sIHF1ZSBlc2EgZWxlY2Npw7NuIG5vIHNlcnZpcsOhIHBhcmEgcmV2b2NhciBlc3RhIGxpY2VuY2lhIG8gcXVlIGRlYmEgc2VyIG90b3JnYWRhICwgYmFqbyBsb3MgdMOpcm1pbm9zIGRlIGVzdGEgbGljZW5jaWEpLCB5IGVzdGEgbGljZW5jaWEgY29udGludWFyw6EgZW4gcGxlbm8gdmlnb3IgeSBlZmVjdG8gYSBtZW5vcyBxdWUgc2VhIHRlcm1pbmFkYSBjb21vIHNlIGV4cHJlc2EgYXRyw6FzLiBMYSBMaWNlbmNpYSByZXZvY2FkYSBjb250aW51YXLDoSBzaWVuZG8gcGxlbmFtZW50ZSB2aWdlbnRlIHkgZWZlY3RpdmEgc2kgbm8gc2UgbGUgZGEgdMOpcm1pbm8gZW4gbGFzIGNvbmRpY2lvbmVzIGluZGljYWRhcyBhbnRlcmlvcm1lbnRlLgo4LiBWYXJpb3MuCmEuCUNhZGEgdmV6IHF1ZSBVc3RlZCBkaXN0cmlidXlhIG8gcG9uZ2EgYSBkaXNwb3NpY2nDs24gcMO6YmxpY2EgbGEgT2JyYSBvIHVuYSBPYnJhIENvbGVjdGl2YSwgZWwgTGljZW5jaWFudGUgb2ZyZWNlcsOhIGFsIGRlc3RpbmF0YXJpbyB1bmEgbGljZW5jaWEgZW4gbG9zIG1pc21vcyB0w6lybWlub3MgeSBjb25kaWNpb25lcyBxdWUgbGEgbGljZW5jaWEgb3RvcmdhZGEgYSBVc3RlZCBiYWpvIGVzdGEgTGljZW5jaWEuCmIuCVNpIGFsZ3VuYSBkaXNwb3NpY2nDs24gZGUgZXN0YSBMaWNlbmNpYSByZXN1bHRhIGludmFsaWRhZGEgbyBubyBleGlnaWJsZSwgc2Vnw7puIGxhIGxlZ2lzbGFjacOzbiB2aWdlbnRlLCBlc3RvIG5vIGFmZWN0YXLDoSBuaSBsYSB2YWxpZGV6IG5pIGxhIGFwbGljYWJpbGlkYWQgZGVsIHJlc3RvIGRlIGNvbmRpY2lvbmVzIGRlIGVzdGEgTGljZW5jaWEgeSwgc2luIGFjY2nDs24gYWRpY2lvbmFsIHBvciBwYXJ0ZSBkZSBsb3Mgc3VqZXRvcyBkZSBlc3RlIGFjdWVyZG8sIGFxdcOpbGxhIHNlIGVudGVuZGVyw6EgcmVmb3JtYWRhIGxvIG3DrW5pbW8gbmVjZXNhcmlvIHBhcmEgaGFjZXIgcXVlIGRpY2hhIGRpc3Bvc2ljacOzbiBzZWEgdsOhbGlkYSB5IGV4aWdpYmxlLgpjLglOaW5nw7puIHTDqXJtaW5vIG8gZGlzcG9zaWNpw7NuIGRlIGVzdGEgTGljZW5jaWEgc2UgZXN0aW1hcsOhIHJlbnVuY2lhZGEgeSBuaW5ndW5hIHZpb2xhY2nDs24gZGUgZWxsYSBzZXLDoSBjb25zZW50aWRhIGEgbWVub3MgcXVlIGVzYSByZW51bmNpYSBvIGNvbnNlbnRpbWllbnRvIHNlYSBvdG9yZ2FkbyBwb3IgZXNjcml0byB5IGZpcm1hZG8gcG9yIGxhIHBhcnRlIHF1ZSByZW51bmNpZSBvIGNvbnNpZW50YS4KZC4JRXN0YSBMaWNlbmNpYSByZWZsZWphIGVsIGFjdWVyZG8gcGxlbm8gZW50cmUgbGFzIHBhcnRlcyByZXNwZWN0byBhIGxhIE9icmEgYXF1w60gbGljZW5jaWFkYS4gTm8gaGF5IGFycmVnbG9zLCBhY3VlcmRvcyBvIGRlY2xhcmFjaW9uZXMgcmVzcGVjdG8gYSBsYSBPYnJhIHF1ZSBubyBlc3TDqW4gZXNwZWNpZmljYWRvcyBlbiBlc3RlIGRvY3VtZW50by4gRWwgTGljZW5jaWFudGUgbm8gc2UgdmVyw6EgbGltaXRhZG8gcG9yIG5pbmd1bmEgZGlzcG9zaWNpw7NuIGFkaWNpb25hbCBxdWUgcHVlZGEgc3VyZ2lyIGVuIGFsZ3VuYSBjb211bmljYWNpw7NuIGVtYW5hZGEgZGUgVXN0ZWQuIEVzdGEgTGljZW5jaWEgbm8gcHVlZGUgc2VyIG1vZGlmaWNhZGEgc2luIGVsIGNvbnNlbnRpbWllbnRvIG11dHVvIHBvciBlc2NyaXRvIGRlbCBMaWNlbmNpYW50ZSB5IFVzdGVkLgo= 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