Brauer Analysis of Thompson’s Group F and Its Application to the Solutions of Some Yang–Baxter Equations

Agustín Moreno Cañadas (), José Gregorio Rodríguez-Nieto, Olga Patricia Salazar-Díaz, Raúl Velásquez and Hernán Giraldo
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Agustín Moreno Cañadas: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
José Gregorio Rodríguez-Nieto: Departamento de Matemáticas, Universidad Nacional de Colombia, Kra 65 No 59A-110, Medellín 050034, Colombia
Olga Patricia Salazar-Díaz: Departamento de Matemáticas, Universidad Nacional de Colombia, Kra 65 No 59A-110, Medellín 050034, Colombia
Raúl Velásquez: Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No 53-108, Medellín 050010, Colombia
Hernán Giraldo: Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No 53-108, Medellín 050010, Colombia

Mathematics, 2025, vol. 13, issue 7, 1-23

Abstract: The study of algebraic invariants associated with Brauer configuration algebras induced by appropriate multisets is said to be a Brauer analysis of the data that define the multisets. In general, giving an explicit description of such invariants as the dimension of the algebras or the dimension of their centers is a hard problem. This paper performs a Brauer analysis on some generators of Thompson’s group F . It proves that such generators and some appropriate Christoffel words induce Brauer configuration algebras whose dimensions are given by the number of edges and vertices of the binary trees defining them. The Brauer analysis includes studying the covering graph induced by a corresponding quiver; this paper proves that these graphs allow for finding set-theoretical solutions of the Yang–Baxter equation.

Keywords: Brauer configuration algebra; Brauer analysis; Christoffel word; path algebra; Thompson’s group; Yang–Baxter equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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