Degenerations of Zinbiel and nilpotent Leibniz algebras

Abstract

We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over C. In particular, we describe all irreducible components in the corresponding varieties.

It is the joint version of the original paper [Linear and Multilinear Algebra, 66 (2018), 4, 704-716] and the corrigendum to the original paper [Linear and Multilinear Algebra, 2020, DOI: 10.1080/03081087.2020.1749543]. arXiv admin note: text overlap with arXiv:1609.07392

References in corpus (4)

• The variety of $2$-dimensional algebras over an algebraically closed field
• Degenerations of binary Lie and nilpotent Malcev algebras
• Classification of 4-dimensional nilpotent complex Leibniz algebras
• Naturally graded Zinbiel algebras with nilindex $n-3$

Cited by in corpus (33)

• The variety of $2$-dimensional algebras over an algebraically closed field
• The algebraic and geometric classification of nilpotent binary Lie algebras
• 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
• Degenerations of binary Lie and nilpotent Malcev algebras
• Degenerations of Leibniz and anticommutative algebras
• The geometric classification of Leibniz algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• Complete classification of algebras of level two
• The classification of $2$-dimensional rigid algebras
• Degenerations of Jordan Superalgebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• Non-associative algebraic structures: classification and structure
• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
• The algebraic classification of nilpotent algebras
• The algebraic classification of nilpotent Tortkara algebras
• Degenerations of Jordan Algebras and ''Marginal'' Algebras
• The geometric classification of nilpotent Tortkara algebras
• Degenerations of Filippov algebras
• The algebraic and geometric classification of Zinbiel algebras
• Some cohomologically rigid solvable Leibniz algebras
• Central extensions of filiform Zinbiel algebras
• Degenerations of nilpotent associative commutative algebras
• Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras
• One-generated nilpotent terminal algebras
• Central extensions of 3-dimensional Zinbiel algebras
• Symmetric Zinbiel superalgebras
• The algebraic and geometric classification of antiassociative algebras
• The algebraic and geometric classification of nilpotent right alternative algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1,1\mid m)$ and nilindex $n+m$