Infinitesimal deformations of naturally graded filiform Leibniz algebras

Abstract

We describe infinitesimal deformations of complex naturally graded filiform Leibniz algebras. It is known that any $n$-dimensional filiform Lie algebra can be obtained by a linear integrable deformation of the naturally graded algebra $F_n^3(0)$. We establish that in the same way any $n$-dimensional filiform Leibniz algebra can be obtained by an infinitesimal deformation of the filiform Leibniz algebras $F_n^1,$ $F_n^2$ and $F_n^3(\alpha )$. Moreover, we describe the linear integrable deformations of above-mentioned algebras with a fixed basis of $H{L}^2$ in the set of all $n$-dimensional Leibniz algebras. Among these deformations we found one new rigid algebra.

16 pages

References in corpus (3)

• Infinitesimal deformations of null-filiform Leibniz superalgebras
• Formal deformations, contractions and moduli spaces of Lie algebras
• Classification of solvable Leibniz algebras with naturally graded filiform nilradical

Cited by in corpus (3)

• Non-associative algebraic structures: classification and structure
• Rota-type operators on null-filiform associative algebras
• Abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras