Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras
Currently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation deals with developing theories such as knot theory, Hopf a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/11/1/2 |
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| author | Agustín Moreno Cañadas Adolfo Ballester-Bolinches Isaías David Marín Gaviria |
| author_facet | Agustín Moreno Cañadas Adolfo Ballester-Bolinches Isaías David Marín Gaviria |
| author_sort | Agustín Moreno Cañadas |
| collection | DOAJ |
| description | Currently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation deals with developing theories such as knot theory, Hopf algebras, quandles, Lie and Jordan (super) algebras, and quantum computing. One of the most successful techniques to obtain solutions of the YBE was given by Rump, who introduced an algebraic structure called the brace, which allows giving non-degenerate involutive set-theoretical solutions. This paper introduces Brauer configuration algebras, which, after appropriate specializations, give rise to braces associated with Thompson’s group <i>F</i>. The dimensions of these algebras and their centers are also given. |
| first_indexed | 2024-03-09T13:08:01Z |
| format | Article |
| id | doaj.art-cdc281dedc594b7d8ecd61d0bb41b750 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T13:08:01Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-cdc281dedc594b7d8ecd61d0bb41b7502023-11-30T21:46:06ZengMDPI AGComputation2079-31972022-12-01111210.3390/computation11010002Solutions of the Yang–Baxter Equation Arising from Brauer Configuration AlgebrasAgustín Moreno Cañadas0Adolfo Ballester-Bolinches1Isaías David Marín Gaviria2Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No. 45-03, Bogotá 11001000, ColombiaDepartament de Matemàtiques, Universitat de València, Dr. Moliner 50, Burjassot, 46100 València, SpainDepartamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No. 45-03, Bogotá 11001000, ColombiaCurrently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation deals with developing theories such as knot theory, Hopf algebras, quandles, Lie and Jordan (super) algebras, and quantum computing. One of the most successful techniques to obtain solutions of the YBE was given by Rump, who introduced an algebraic structure called the brace, which allows giving non-degenerate involutive set-theoretical solutions. This paper introduces Brauer configuration algebras, which, after appropriate specializations, give rise to braces associated with Thompson’s group <i>F</i>. The dimensions of these algebras and their centers are also given.https://www.mdpi.com/2079-3197/11/1/2braceBrauer configuration algebrapath algebraYang–Baxter equation |
| spellingShingle | Agustín Moreno Cañadas Adolfo Ballester-Bolinches Isaías David Marín Gaviria Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras Computation brace Brauer configuration algebra path algebra Yang–Baxter equation |
| title | Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras |
| title_full | Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras |
| title_fullStr | Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras |
| title_full_unstemmed | Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras |
| title_short | Solutions of the Yang–Baxter Equation Arising from Brauer Configuration Algebras |
| title_sort | solutions of the yang baxter equation arising from brauer configuration algebras |
| topic | brace Brauer configuration algebra path algebra Yang–Baxter equation |
| url | https://www.mdpi.com/2079-3197/11/1/2 |
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