Brauer Analysis of Thompson’s Group F and Its Application to the Solutions of Some Yang–Baxter Equations
Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13071127
Institutions: Universidad Nacional de Colombia, Universidad de Antioquia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4408996006