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...
- 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
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/84376
- Palabra clave:
- 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
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | 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) |
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