Extended Brauer analysis of some Dynkin and Euclidean diagrams
The analysis of algebraic invariants of algebras induced by appropriated multiset systems called Brauer configurations is a Brauer analysis of the data defining the multisets. Giving a complete description of such algebraic invariants (e.g., giving a closed formula for the dimensions of algebras ind...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-10-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024266 |
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| author | Agustín Moreno Cañadas Pedro Fernando Fernández Espinosa José Gregorio Rodríguez-Nieto Odette M Mendez Ricardo Hugo Arteaga-Bastidas |
| author_facet | Agustín Moreno Cañadas Pedro Fernando Fernández Espinosa José Gregorio Rodríguez-Nieto Odette M Mendez Ricardo Hugo Arteaga-Bastidas |
| author_sort | Agustín Moreno Cañadas |
| collection | DOAJ |
| description | The analysis of algebraic invariants of algebras induced by appropriated multiset systems called Brauer configurations is a Brauer analysis of the data defining the multisets. Giving a complete description of such algebraic invariants (e.g., giving a closed formula for the dimensions of algebras induced by significant classes of Brauer configurations) is generally a tricky problem. Ringel previously proposed an analysis of this type in the case of Dynkin algebras, for which so-called Dynkin functions were used to study the numerical behavior of invariants associated with such algebras. This paper introduces two additional tools (the entropy and the covering graph of a Brauer configuration) for Brauer analysis, which is applied to Dynkin and Euclidean diagrams to define Dynkin functions associated with Brauer configuration algebras. Properties of graph entropies defined by the corresponding covering graphs are given to establish relationships between the theory of Dynkin functions, the Brauer configuration algebras theory, and the topological content information theory. |
| format | Article |
| id | doaj-art-d25024da04244822888e1db03b0dc89c |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-d25024da04244822888e1db03b0dc89c2025-01-23T07:52:53ZengAIMS PressElectronic Research Archive2688-15942024-10-0132105752578210.3934/era.2024266Extended Brauer analysis of some Dynkin and Euclidean diagramsAgustín Moreno Cañadas0Pedro Fernando Fernández Espinosa1José Gregorio Rodríguez-Nieto2Odette M Mendez3Ricardo Hugo Arteaga-Bastidas4Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, ColombiaDepartamento de Matemáticas, Universidad de Caldas, Calle 65 No 26-10, Manizales, ColombiaDepartamento de Matemáticas, Universidad Nacional de Colombia, Kra 65 No 59A-110, Medellín, ColombiaDepartamento de Matemáticas, Universidad Nacional de Colombia, Sede La Nubia, Manizales, ColombiaDepartamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, ColombiaThe analysis of algebraic invariants of algebras induced by appropriated multiset systems called Brauer configurations is a Brauer analysis of the data defining the multisets. Giving a complete description of such algebraic invariants (e.g., giving a closed formula for the dimensions of algebras induced by significant classes of Brauer configurations) is generally a tricky problem. Ringel previously proposed an analysis of this type in the case of Dynkin algebras, for which so-called Dynkin functions were used to study the numerical behavior of invariants associated with such algebras. This paper introduces two additional tools (the entropy and the covering graph of a Brauer configuration) for Brauer analysis, which is applied to Dynkin and Euclidean diagrams to define Dynkin functions associated with Brauer configuration algebras. Properties of graph entropies defined by the corresponding covering graphs are given to establish relationships between the theory of Dynkin functions, the Brauer configuration algebras theory, and the topological content information theory.https://www.aimspress.com/article/doi/10.3934/era.2024266brauer configuration algebra (bca)dynkin diagramdynkin functioneuclidean diagramgraph entropyinteger categorificationpath algebraquiver representation |
| spellingShingle | Agustín Moreno Cañadas Pedro Fernando Fernández Espinosa José Gregorio Rodríguez-Nieto Odette M Mendez Ricardo Hugo Arteaga-Bastidas Extended Brauer analysis of some Dynkin and Euclidean diagrams Electronic Research Archive brauer configuration algebra (bca) dynkin diagram dynkin function euclidean diagram graph entropy integer categorification path algebra quiver representation |
| title | Extended Brauer analysis of some Dynkin and Euclidean diagrams |
| title_full | Extended Brauer analysis of some Dynkin and Euclidean diagrams |
| title_fullStr | Extended Brauer analysis of some Dynkin and Euclidean diagrams |
| title_full_unstemmed | Extended Brauer analysis of some Dynkin and Euclidean diagrams |
| title_short | Extended Brauer analysis of some Dynkin and Euclidean diagrams |
| title_sort | extended brauer analysis of some dynkin and euclidean diagrams |
| topic | brauer configuration algebra (bca) dynkin diagram dynkin function euclidean diagram graph entropy integer categorification path algebra quiver representation |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024266 |
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