The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras

Abstract

An algebraic classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras is given. This classification is based on an algebraic classification of complex $5$-dimensional nilpotent Jordan algebras.

arXiv commentarXiv admin note: text overlap with arXiv:2006.00734, arXiv:2106.00336, arXiv:2004.03598, arXiv:2008.01554

References in corpus (22)

• 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
• The algebraic and geometric classification of nilpotent bicommutative algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• Non-associative central extensions of null-filiform associative algebras
• Classification of bilinear maps with radical of codimension 2
• The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator
• The classification of $2$-dimensional rigid algebras
• The variety of dual mock-Lie algebras
• The algebraic classification of nilpotent Tortkara algebras
• The algebraic classification of nilpotent algebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• Central extensions of filiform associative algebras
• On a ternary generalization of Jordan algebras
• Central extensions of filiform Zinbiel algebras
• One-generated nilpotent Novikov algebras
• One-generated nilpotent terminal algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras

Cited by in corpus (3)

• The algebraic classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic classification of nilpotent commutative algebras
• The geometric classification of nilpotent commutative $\mathfrak{CD}$-algebras