The variety of dual mock-Lie algebras

Abstract

We classify all complex $7$- and $8$-dimensional dual mock-Lie algebras by algebraic and geometric way. Also we find all non-trivial complex $9$-dimensional dual mock-Lie algebras.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1905.05361 and text overlap with arXiv:1907.00685

References in corpus (12)

• Six-dimensional nilpotent Lie algebras
• The variety of $2$-dimensional algebras over an algebraically closed field
• Classification of five-dimensional nilpotent Jordan algebras
• 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 binary Lie and nilpotent Malcev algebras
• Degenerations of Leibniz and anticommutative algebras
• The geometric classification of Leibniz algebras
• Special and exceptional mock-Lie algebras
• Complete classification of algebras of level two
• The geometric classification of nilpotent Tortkara algebras

Cited by in corpus (11)

• The algebraic and geometric classification of transposed Poisson algebras
• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
• One-generated nilpotent Novikov algebras
• Central extensions of 3-dimensional Zinbiel algebras
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic and geometric classification of nilpotent left-symmetric algebras
• The algebraic and geometric classification of antiassociative algebras
• The algebraic classification of nilpotent Novikov algebras
• One-generated nilpotent assosymmetric algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• Conservative algebras of $2$-dimensional algebras, IV