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

Abstract

We give a geometric classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras. The corresponding geometric variety has dimension $24$ and decomposes into $10$ irreducible components determined by the Zariski closures of a two-parameter family of algebras, three one-parameter families of algebras, and $6$ rigid algebras.

arXiv admin note: substantial text overlap with arXiv:2007.01829, arXiv:2103.01036, arXiv:2001.00253, arXiv:2006.00734; text overlap with arXiv:2109.00483

References in corpus (3)

• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• On anticommutative algebras for which $[R_a,R_b]$ is a derivation
• The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras

Cited by in corpus (1)

• The algebraic and geometric classification of derived Jordan and bicommutative algebras