Algebra Structures Arising from Yang-Baxter Systems

TL;DR

This paper explores how algebra structures related to Yang-Baxter systems can be constructed from algebra factorisations, expanding the understanding of their interconnections in algebraic theory.

Contribution

It introduces a method to construct algebra factorisations from Yang-Baxter systems, linking these concepts in a novel way.

Findings

Established a construction method for algebra factorisations from Yang-Baxter systems

Connected Yang-Baxter systems with algebra factorisations in a new framework

Extended the theoretical understanding of algebra structures related to Yang-Baxter operators

Abstract

Yang-Baxter operators from algebra structures appeared for the first time in [16], [17] and [8]. Later, Yang-Baxter systems from entwining structures were constructed in [5]. In this paper we show that an algebra factorisation can be constructed from a Yang-Baxter system.