Central extensions of 3-dimensional Zinbiel algebras

Abstract

We describe all central extensions of all $3$-dimensional non-zero complex Zinbiel algebras. As a corollary, we have a full classification of $4$-dimensional non-trivial complex Zinbiel algebras and a full classification of $5$-dimensional non-trivial complex Zinbiel algebras with $2$-dimensional annihilator, which gives the principal step in the algebraic classification of $5$-dimensional Zinbiel algebras.

arXiv commentarXiv admin note: text overlap with arXiv:2009.00988

References in corpus (26)

• Six-dimensional nilpotent Lie algebras
• 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 algebraic and geometric classification of nilpotent bicommutative algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• Non-associative central extensions of null-filiform associative algebras
• Classification of bilinear maps with radical of codimension 2
• The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator
• The classification of $2$-dimensional rigid algebras
• The variety of dual mock-Lie algebras
• Time-warping invariants of multidimensional time series
• The algebraic classification of nilpotent algebras
• The algebraic classification of nilpotent Tortkara algebras
• Central extensions of filiform associative algebras
• Cup-product for equivariant Leibniz cohomology and zinbiel algebras
• The geometric classification of nilpotent Tortkara algebras
• Identities of dual Leibniz algebras
• Deformation of dual Leibniz algebra morphisms
• On tortkara triple systems
• Cup-product in Hom-Leibniz cohomology and Hom-Zinbiel algebras
• Central extensions of filiform Zinbiel algebras
• One-generated nilpotent terminal algebras
• Areas of areas generate the shuffle algebra

Cited by in corpus (3)

• Non-associative algebraic structures: classification and structure
• The algebraic and geometric classification of Zinbiel algebras
• Symmetric Zinbiel superalgebras