The algebraic and geometric classification of nilpotent binary Lie algebras

Abstract

The paper is devoted to give the complete algebraic classification of nilpotent binary Lie algebras of dimension $\le 6$ over an arbitrary base field $\mathbb{F}$ of characteristic not $2$ and the complete geometric classification of nilpotent binary Lie algebras of dimension $6$ over $\mathbb{C}.$ As an application, we have the algebraic and geometric classification of nilpotent anticommutative $\mathfrak{CD}$-algebras of dimension $\le 6.$

arXiv commentarXiv admin note: text overlap with arXiv:1812.01442

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Cited by in corpus (27)

• The algebraic and geometric classification of nilpotent Novikov algebras
• The algebraic and geometric classification of nilpotent anticommutative algebras
• Degenerations of nilpotent 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
• The variety of dual mock-Lie algebras
• The algebraic classification of nilpotent algebras
• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
• Non-associative algebraic structures: classification and structure
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• The algebraic classification of nilpotent Tortkara algebras
• The geometric classification of nilpotent Tortkara algebras
• Central extensions of filiform Zinbiel algebras
• Degenerations of nilpotent associative commutative algebras
• One-generated nilpotent Novikov algebras
• One-generated nilpotent terminal algebras
• One-generated nilpotent bicommutative algebras
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• Central extensions of 3-dimensional Zinbiel algebras
• On structured spaces and their properties
• On anticommutative algebras for which $[R_a,R_b]$ is a derivation
• The algebraic and geometric classification of nilpotent right alternative algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• One-generated nilpotent assosymmetric algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• The geometric classification of nilpotent commutative $\mathfrak{CD}$-algebras