The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator

Abstract

We give the classification of all $n$-dimensional anticommutative complex algebras with $(n-3)$-dimensional annihilator. Namely, we describe all central extensions of all $3$-dimensional anticommutative complex algebras.

References in corpus (2)

• Classification of five-dimensional nilpotent Jordan algebras
• Nilpotent evolution algebras over arbitrary fields

Cited by in corpus (19)

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• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent Novikov algebras
• Degenerations of nilpotent algebras
• The algebraic and geometric classification of nilpotent bicommutative algebras
• Degenerations of Leibniz and anticommutative algebras
• Non-associative central extensions of null-filiform associative algebras
• Classification of bilinear maps with radical of codimension 2
• The algebraic classification of nilpotent Tortkara algebras
• The algebraic classification of nilpotent algebras
• Non-associative algebraic structures: classification and structure
• Central extensions of filiform associative algebras
• Central extensions of filiform Zinbiel algebras
• One-generated nilpotent Novikov algebras
• One-generated nilpotent bicommutative algebras
• Central extensions of 3-dimensional Zinbiel algebras
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• One-generated nilpotent assosymmetric algebras