The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

Abstract

We give algebraic and geometric classifications of complex $4$-dimensional nilpotent noncommutative Jordan algebras. Specifically, we find that, up to isomorphism, there are only $18$ non-isomorphic nontrivial nilpotent noncommutative Jordan algebras. The corresponding geometric variety is determined by the Zariski closure of $3$ rigid algebras and $2$ one-parametric families of algebras.

arXiv commentarXiv admin note: text overlap with arXiv:1909.00358 and substantial text overlap with arXiv:1812.01442

References in corpus (16)

• Six-dimensional nilpotent Lie algebras
• The variety of $2$-dimensional algebras over an algebraically closed field
• Classification of five-dimensional nilpotent Jordan algebras
• Degenerations of Zinbiel and nilpotent Leibniz 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 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 geometric classification of Leibniz algebras
• Complete classification of algebras of level two
• The geometric classification of nilpotent Tortkara algebras
• Degenerations of nilpotent associative commutative algebras
• The structure of simple noncommutative Jordan superalgebras

Cited by in corpus (8)

• The algebraic and geometric classification of nilpotent bicommutative algebras
• Non-associative algebraic structures: classification and structure
• One-generated nilpotent bicommutative algebras
• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic and geometric classification of nilpotent right alternative algebras
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras
• The geometric classification of nilpotent commutative $\mathfrak{CD}$-algebras