The algebraic and geometric classification of nilpotent bicommutative algebras

Abstract

We classify the $4$-dimensional nilpotent bicommutative algebras over $\mathbb{C}$ from both algebraic and geometric approaches.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1812.01442

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Cited by in corpus (22)

• 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 terminal algebras
• Non-associative central extensions of null-filiform associative algebras
• The algebraic classification of nilpotent algebras
• The algebraic classification of nilpotent Tortkara algebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• Non-associative algebraic structures: classification and structure
• Degenerations of Filippov algebras
• The geometric classification of nilpotent algebras
• One-generated nilpotent Novikov algebras
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• One-generated nilpotent bicommutative algebras
• Central extensions of 3-dimensional Zinbiel algebras
• One-generated nilpotent terminal algebras
• The algebraic and geometric classification of nilpotent right alternative algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• One-generated nilpotent assosymmetric algebras
• The algebraic and geometric classification of derived Jordan and bicommutative algebras
• Gelfand-Kirillov dimension of bicommutative algebras