The algebraic classification of nilpotent commutative algebras

Abstract

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller nilpotent commutative algebras and the recently obtained classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2109.00483; text overlap with arXiv:2106.00336, arXiv:2004.03598

References in corpus (8)

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

Cited by in corpus (2)

• The algebraic and geometric classification of transposed Poisson algebras
• Non-associative algebraic structures: classification and structure