From Braces to Hecke algebras & Quantum Groups
Mathematical Physics
2022-06-30 v3 Group Theory
math.MP
Quantum Algebra
Rings and Algebras
Abstract
We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras and we identify new quantum groups associated to set-theoretic solutions coming from braces. We also construct a novel class of quantum discrete integrable systems and we derive symmetries for the corresponding periodic transfer matrices.
Cite
@article{arxiv.1912.03091,
title = {From Braces to Hecke algebras & Quantum Groups},
author = {Anastasia Doikou and Agata Smoktunowicz},
journal= {arXiv preprint arXiv:1912.03091},
year = {2022}
}
Comments
25 pages, LaTex. Clarifying comments added, a few typos corrected. E-pub ahead of print in: Journal of Algebra and its Applications