Degenerations of nilpotent algebras

Abstract

We give a complete description of degenerations of $3$-dimensional nilpotent algebras, $4$-dimensional nilpotent commutative algebras and $5$-dimensional nilpotent anticommutative algebras over $\mathbb{C}$. In particular, we correct several mistakes from the paper `Contractions of low-dimensional nilpotent Jordan algebras' by Ancochea Bermúdez, Fresán and Margalef Bentabol.

arXiv commentarXiv admin note: text overlap with arXiv:1808.00907, arXiv:1611.06454

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• 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
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• The algebraic and geometric classification of nilpotent Novikov algebras
• The algebraic and geometric classification of nilpotent anticommutative algebras
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• Degenerations of Jordan Superalgebras
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Cited by in corpus (14)

• The algebraic and geometric classification of nilpotent Novikov algebras
• The algebraic and geometric classification of nilpotent anticommutative 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 algebraic classification of nilpotent algebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• Transposed Poisson structures
• The algebraic and geometric classification of Zinbiel algebras
• The geometric classification of nilpotent algebras
• One-generated nilpotent bicommutative algebras
• The algebraic classification of nilpotent commutative algebras
• The geometric classification of nilpotent commutative $\mathfrak{CD}$-algebras
• Conservative algebras of $2$-dimensional algebras, IV