## Journal of Generalized Lie Theory and Applications

### Infinitesimal Deformations of the Model ${\mathbb{Z}_3}$-Filiform Lie Algebra

Rosa María Navarro

#### 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 Lie 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.

#### Article information

Source
J. Gen. Lie Theory Appl., Volume 7 (2013), 11 pages.

Dates
First available in Project Euclid: 23 July 2015

https://projecteuclid.org/euclid.jglta/1437656918

Digital Object Identifier
doi:10.4303/jglta/235699

Mathematical Reviews number (MathSciNet)
MR3038861

Zentralblatt MATH identifier
1317.17018

#### Citation

Navarro, Rosa María. Infinitesimal Deformations of the Model ${\mathbb{Z}_3}$-Filiform Lie Algebra. J. Gen. Lie Theory Appl. 7 (2013), 11 pages. doi:10.4303/jglta/235699. https://projecteuclid.org/euclid.jglta/1437656918