From braces to Hecke algebras and quantum groups

Anastasia Doikou, Agata Smoktunowicz

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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.
Original languageEnglish
Article number2350179
JournalJournal of Algebra and its Applications
Early online date31 May 2022
DOIs
Publication statusE-pub ahead of print - 31 May 2022

Keywords

  • Yang-Baxter equation
  • braces
  • braid groups
  • quantum algebras

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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