The classification of $2$-dimensional rigid algebras

Abstract

Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the geometric classification of the variety of $2$-dimensional terminal algebras, and based on the geometric classification of these algebras we formulate some open problems.

References in corpus (6)

• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Degenerations of binary Lie and nilpotent Malcev algebras
• The geometric classification of Leibniz algebras
• Conservative algebras of 2-dimensional algebras
• Conservative algebras of $2$-dimensional algebras, II
• On The Kantor Product

Cited by in corpus (19)

• 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
• The algebraic and geometric classification of nilpotent terminal algebras
• The algebraic classification of nilpotent Tortkara algebras
• Non-associative algebraic structures: classification and structure
• The geometric classification of nilpotent Tortkara algebras
• Central extensions of filiform Zinbiel algebras
• Degenerations of nilpotent associative commutative algebras
• One-generated nilpotent Novikov algebras
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• One-generated nilpotent terminal algebras
• Central extensions of 3-dimensional Zinbiel algebras
• The universal conservative superalgebra
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• One-generated nilpotent assosymmetric algebras
• Conservative algebras of $2$-dimensional algebras, IV