Degenerations of Leibniz and anticommutative algebras

Abstract

We describe all degenerations of three dimensional anticommutative algebras ${\mathfrak{Acom}}_3$ and of three dimensional Leibniz algebras ${\mathfrak{Leib}}_3$ over $\mathbb{C}.$ In particular, we describe all irreducible components and rigid algebras in the corresponding varieties

arXiv commentarXiv admin note: substantial text overlap with arXiv:1611.06454, arXiv:1707.08836, arXiv:1705.04346

References in corpus (7)

• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Canonical matrices of bilinear and sesquilinear forms
• Degenerations of binary Lie and nilpotent Malcev algebras
• The geometric classification of Leibniz algebras
• Complete classification of algebras of level two
• The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator
• Degenerations of Jordan Superalgebras

Cited by in corpus (20)

• 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
• Complete classification of algebras of level two
• The variety of dual mock-Lie algebras
• The algebraic and geometric classification of transposed Poisson algebras
• Non-associative algebraic structures: classification and structure
• The algebraic classification of nilpotent algebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• The algebraic classification of nilpotent Tortkara algebras
• The geometric classification of nilpotent Tortkara algebras
• Degenerations of Filippov algebras
• Degenerations of nilpotent associative commutative algebras
• On the Kantor product, II
• Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras
• The algebraic and geometric classification of nilpotent left-symmetric algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic and geometric classification of nilpotent right alternative algebras
• Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1,1\mid m)$ and nilindex $n+m$