Cohomologies and linear deformations of pre-Jacobi-Jordan algebras

TL;DR

This paper develops a cohomology theory for left pre-Jacobi-Jordan algebras and explores their linear deformations, introducing Nijenhuis operators and demonstrating their role in trivial deformations.

Contribution

It introduces a cohomology framework for pre-Jacobi-Jordan algebras and analyzes deformations using Nijenhuis operators, which was not previously studied.

Findings

Cohomology theory for pre-Jacobi-Jordan algebras established

Nijenhuis operators generate trivial deformations

Deformation theory for these algebras developed

Abstract

The purpose of this paper is to introduce an algebraic cohomology theory of left pre-Jacobi-Jordan algebras. We use the cohomological approach to study linear deformations of these algebras. We also introduce the notion of Nijenhuis operators on pre-Jacobi-Jordan algebras and we show that the deformation generated by a Nijenhuis operator is trivial.