Quasi-commutative algebras

TL;DR

This paper characterizes quasi-commutative algebras, which are commutative relative to a Yang-Baxter operator, using cosimplicial complexes, enabling classification of such structures in certain cases.

Contribution

It introduces a new characterization of quasi-commutative algebras via cosimplicial complexes, facilitating their classification.

Findings

Characterization of quasi-commutative algebras using cosimplicial complexes

Classification of quasi-commutative structures in specific cases

Linking algebraic properties to topological constructs

Abstract

We characterise algebras commutative with respect to a Yang-Baxter operator (quasi-commutative algebras) in terms of certain cosimplicial complexes. In some cases this characterisation allows the classification of all possible quasi-commutative structures.