Cohomology of BiHom-Associative Trialgebras

TL;DR

This paper develops a cohomology theory for BiHom-associative trialgebras, linking central extensions, deformations, and derivations, thereby unifying existing algebraic structures and advancing their mathematical understanding.

Contribution

It introduces a unified cohomology framework for BiHom-associative trialgebras and classifies their deformations and derivations, extending prior algebraic theories.

Findings

Established correspondence between central extensions and second cohomology.

Developed a general cohomology theory unifying previous algebraic structures.

Classified generalized αβ-derivations of 3-dimensional BiHom-associative trialgebras.

Abstract

The paper concerns the cohomology of (multiplicative) BiHom-associative trialgebras. We first detail the correspondence between central extensions and second cohomology. This is followed by a general cohomology theory that unifies those of BiHom-associative algebras and associative trialgebras. Finally, we introduce one-parameter formal deformations and classify generalized $\alpha\beta$-derivations of 3-dimensional BiHom-associative trialgebras.