Deformations of some Color Lie Superalgebras

TL;DR

This paper investigates the infinitesimal deformations of a specific class of color Lie superalgebras, showing how all such algebras can be generated through these deformations and providing a family of examples.

Contribution

It characterizes all filiform $ ext{Z}_2 imes ext{Z}_2$-color Lie superalgebras via infinitesimal deformations and constructs a family of these algebras through linearly integrable deformations.

Findings

All filiform $ ext{Z}_2 imes ext{Z}_2$-color Lie superalgebras can be obtained by infinitesimal deformations.

A specific family of filiform $ ext{Z}_2 imes ext{Z}_2$-color Lie superalgebras is constructed.

Infinitesimal deformations are crucial for understanding the structure of these superalgebras.

Abstract

In this work infinitesimal deformations of the model filiform $\mathbb{Z}_2 \times \mathbb{Z}_2$-color Lie superalgebra have been studied. All the filiform $\mathbb{Z}_2 \times \mathbb{Z}_2$-color Lie superalgebras can be obtained by means of infinitesimal deformations, hence the importance of these. Thus, in particular, we give a family of filiform $\mathbb{Z}_2 \times \mathbb{Z}_2$-color Lie superalgebras via linearly integrable deformations.