From Braces to Hecke algebras & Quantum Groups

TL;DR

This paper explores the connections between braces, set-theoretic solutions of the Yang-Baxter equation, and quantum groups, introducing new algebraic structures and integrable systems in the context of quantum algebra.

Contribution

It establishes links between braces and quantum groups, identifies new quantum groups from set-theoretic solutions, and constructs novel quantum integrable systems.

Findings

Identified new quantum groups associated with braces

Constructed a new class of quantum discrete integrable systems

Derived symmetries for periodic transfer matrices

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.