Deformations of relative Rota-Baxter operators on Hom-Jacobi-Jordan algebras

TL;DR

This paper develops a cohomology theory for Hom-Jacobi-Jordan algebras and their relative Rota-Baxter operators, applying it to study algebra deformations and operator deformations.

Contribution

It introduces a cohomology framework for Hom-Jacobi-Jordan algebras and relative Rota-Baxter operators, enabling systematic deformation analysis.

Findings

Cohomology theory for Hom-Jacobi-Jordan algebras established

Deformations of algebras and operators analyzed using cohomology

Applications include derivations and central extensions

Abstract

Representations of Hom-Jacobi-Jordan algebras are studied. In particular, adjoint representations and trivial representations are studied in detail. Derivations and central extensions of Hom-Jacobi-Jordan algebras are also discussed as an application. Morover, we introduce the cohomology theory on Hom-Jacobi-Jordan algebras as well as the one of relative Rota-Baxter operators on Hom-Jacobi-Jordan algebras. Finally, we use the cohomological approach to study deformations of Hom-Jacobi-Jordan algebras and those of relative Rota-Baxter operators.