Infinitesimal Deformations of the Model $\mathbb{Z}-3$-Filiform Lie Algebra

Source: J. Gen. Lie Theory Appl., Volume 7, 11 pages.

Abstract:
In this work, it is considered that the vector space is 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 algebras can be obtained, hence the importance of these deformations. The results obtained in this work, together with those obtained by Khakimdjanov and Navarro ( J. Geom. Phys. 2011 and 2012), lead to compute the total dimension of the mentioned space of deformations.