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.
Highlights
The concept of filiform Lie algebras was firstly introduced in [18] by Vergne. This type of nilpotent Lie algebra has important properties; in particular, every filiform Lie algebra can be obtained by a deformation of the model filiform algebra Ln
In the same way as filiform Lie algebras, all filiform Lie superalgebras can be obtained by infinitesimal deformations of the model Lie superalgebra Ln,m [1], [4], [8] and [9]
We have studied the infinitesimal deformations of the model Z3-color Lie superalgebra, i.e. the model Z3-filiform Lie algebra Ln,m,p
Summary
The concept of filiform Lie algebras was firstly introduced in [18] by Vergne. This type of nilpotent Lie algebra has important properties; in particular, every filiform Lie algebra can be obtained by a deformation of the model filiform algebra Ln. A representation of a (G, β)-color Lie superalgebra is a mapping ρ : L −→ End(V ), where V = g∈G Vg is a graded vector space such that
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More From: Journal of Generalized Lie Theory and Applications
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