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

References in corpus (13)

• Six-dimensional nilpotent Lie algebras
• The variety of $2$-dimensional algebras over an algebraically closed field
• Classification of five-dimensional nilpotent Jordan algebras
• Degenerations of Zinbiel and nilpotent Leibniz algebras
• The algebraic and geometric classification of nilpotent binary Lie algebras
• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent Novikov algebras
• The classification of $2$-dimensional rigid algebras
• The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator
• Central extensions of filiform associative algebras
• Cup-product for equivariant Leibniz cohomology and zinbiel algebras
• The geometric classification of nilpotent Tortkara algebras
• Deformation of dual Leibniz algebra morphisms

Cited by in corpus (4)

• One-generated nilpotent bicommutative algebras
• Central extensions of 3-dimensional Zinbiel algebras
• One-generated nilpotent assosymmetric algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras