Complete classification of algebras of level two

Abstract

The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e. such algebras that maximal chains of nontrivial degenerations starting at them have length two. During this classification we obtain an estimation of the level of an algebra via its generation type, i.e. the maximal dimension of its one generated subalgebra. Also we describe all degenerations and levels of algebras of the generation type $1$ with a square zero ideal of codimension $1$.

References in corpus (7)

• The variety of $2$-dimensional algebras over an algebraically closed field
• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Degenerations of binary Lie and nilpotent Malcev algebras
• Degenerations of Leibniz and anticommutative algebras
• The classification of algebras of level two
• Classification of algebras of level two in the variety of nilpotent algebras and Leibniz algebras
• On degenerations of algebras over an arbitrary field

Cited by in corpus (19)

• 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
• Degenerations of nilpotent algebras
• The algebraic and geometric classification of nilpotent bicommutative algebras
• Degenerations of Leibniz and anticommutative algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• The variety of dual mock-Lie algebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• Non-associative algebraic structures: classification and structure
• Degenerations of Jordan Algebras and ''Marginal'' Algebras
• The geometric classification of nilpotent Tortkara algebras
• Degenerations of Filippov algebras
• Degenerations of nilpotent associative commutative algebras
• The geometric classification of nilpotent algebras
• One-generated nilpotent terminal algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic and geometric classification of nilpotent right alternative algebras
• The geometric classification of $2$-step nilpotent algebras and applications