Journal of Generalized Lie Theory and Applications

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

Rosa María Navarro

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1437656918

Digital Object Identifier
doi:10.4303/jglta/235699

Mathematical Reviews number (MathSciNet)
MR3038861

Zentralblatt MATH identifier
1317.17018

Subjects
Primary: 17B30: Solvable, nilpotent (super)algebras 17B70: Graded Lie (super)algebras 17B75: Color Lie (super)algebras 17B56: Cohomology of Lie (super)algebras

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


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