Leibniz algebras associated with representations of filiform Lie algebras

Abstract

In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra $n_{n,1}.$ We introduce a Fock module for the algebra $n_{n,1}$ and provide classification of Leibniz algebras $L$ whose corresponding Lie algebra $L/I$ is the algebra $n_{n,1}$ with condition that the ideal $I$ is a Fock $n_{n,1}$-module, where $I$ is the ideal generated by squares of elements from $L$.

15 pages

References in corpus (2)

• Algebraic curves for commuting elements in the q-deformed Heisenberg algebra
• Leibniz algebras of Heisenberg type

Cited by in corpus (3)

• Leibniz algebras associated with representations of Euclidean Lie algebra
• Leibniz algebras associated with representations of the Diamond Lie algebra
• Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type ${\mathcal{L}}^4$