Extensions of (metric) Hom-Jacobi-Jordan algebras

TL;DR

This paper develops a second cohomology theory for (metric) Hom-Jacobi-Jordan algebras and demonstrates its role in classifying abelian extensions, advancing the algebraic understanding of these structures.

Contribution

It introduces a second cohomology group for (metric) Hom-Jacobi algebras and proves its use in classifying abelian extensions, providing new tools for algebraic analysis.

Findings

Defined second cohomology group for (metric) Hom-Jacobi algebras

Proved classification of abelian extensions via second cohomology

Enhanced understanding of algebraic extensions in Hom-Jacobi structures

Abstract

The main purpose of this paper is to provide a second cohomology group of a (metric) Hom-Jacobi algebra with coefficients in a given representation. Moreover, we show that second cohomology group classifies abelian extensions of a (metric) Hom-Jacobi algebra algebra by a representation.