Infinitesimal deformations of the model $\mathbb{Z}_3$-filiform Lie algebra

TL;DR

This paper studies the infinitesimal deformations of a specific $ ext{Z}_3$-filiform Lie algebra, showing how these deformations generate all such algebras and calculating the dimension of the deformation space.

Contribution

It characterizes the space of infinitesimal deformations of the model $ ext{Z}_3$-filiform Lie algebra and computes its total dimension, linking to previous deformation results.

Findings

Deformation space dimension computed

All $ ext{Z}_3$-filiform Lie algebras obtained from the model

Connection established with previous deformation studies

Abstract

In this work it is considered the vector space composed by the infinitesimal deformations of the model $\mathbb{Z}_3$-filiform Lie algebra $L^{n,m,p}$. By using these deformations all the $\mathbb{Z}_3$-filiform Lie algebras can be obtained, hence the importance of these deformations. The results obtained in this work together to those obtained in [Integrable deformations of nilpotent color Lie superalgebras, J. Geom. Phys. 61(2011)1797-1808] and [Corrigendum to Integrable deformations of nilpotent color Lie superalgebras, J. Geom. Phys. 62(2012)1571], leads to compute the total dimension of the mentioned space of deformations.