Semi-entwining structures and their applications

TL;DR

This paper introduces semi-entwining structures as simpler alternatives to entwining structures, demonstrating their usefulness in algebraic constructions and solutions to Yang-Baxter systems.

Contribution

It defines semi-entwining structures and explores their applications, including constructing intertwining operators, braided algebras, and solutions to Yang-Baxter systems.

Findings

Semi-entwining structures are simpler than entwining structures.

They can be used to construct intertwining operators and braided algebras.

Applications include lifting functors and solving Yang-Baxter systems.

Abstract

Semi-entwining structures are proposed as concepts simpler than entwining structures, yet they are shown to have interesting applications in constructing intertwining operators and braided algebras, lifting functors, finding solutions for Yang-Baxter systems, etc. While for entwining structures one can associate corings, for semi-entwining structures one can associate comodule algebra structures where the algebra involved is a bialgebra satisfying certain properties.