Central extensions of filiform Zinbiel algebras

Abstract

In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform Zinbiel algebras. It is proven that every non-split central extension of an $n$-dimensional null-filiform Zinbiel algebra is isomorphic to an $(n+1)$-dimensional null-filiform Zinbiel algebra. Moreover, we obtain all pairwise non isomorphic quasi-filiform Zinbiel algebras.

arXiv admin note: substantial text overlap with arXiv:1809.00183, arXiv:1904.00845, arXiv:1812.01442, arXiv:1803.07698

References in corpus (1)

• Deformation of dual Leibniz algebra morphisms

Cited by in corpus (2)

• One-generated nilpotent assosymmetric algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras