The geometric classification of Leibniz algebras

Abstract

We describe all rigid algebras and all irreducible components in the variety of four dimensional Leibniz algebras ${\mathfrak{Leib}}_4$ over $\mathbb{C}.$ In particular, we prove that the Grunewald--O'Halloran conjecture is not valid and the Vergne conjecture is valid for ${\mathfrak{Leib}}_4.$

It is the correction of the published version. The classification of irreducible components and rigid algebras is improved. Namely, the algebra ${\mathfrak{L}}_2$ is not rigid

References in corpus (2)

• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Degenerations of binary Lie and nilpotent Malcev algebras

Cited by in corpus (26)

• 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 anticommutative algebras
• The algebraic and geometric classification of nilpotent Novikov 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 algebraic and geometric classification of nilpotent terminal algebras
• The classification of $2$-dimensional rigid algebras
• The variety of dual mock-Lie algebras
• Degenerations of Jordan Superalgebras
• The algebraic classification of nilpotent algebras
• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• The geometric classification of nilpotent Tortkara algebras
• Degenerations of Filippov algebras
• Some cohomologically rigid solvable Leibniz algebras
• Degenerations of nilpotent associative commutative algebras
• The geometric classification of nilpotent algebras
• One-generated nilpotent terminal algebras
• The algebraic and geometric classification of nilpotent left-symmetric algebras
• The algebraic and geometric classification of nilpotent right alternative algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• One-generated nilpotent assosymmetric algebras
• Abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras