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.
Categories: math.RT