English

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.

Keywords

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

R2 v1 2026-06-23T12:37:58.114Z