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

Abstract

We give a geometric classification of complex $4$-dimensional nilpotent $\mathfrak{CD}$-algebras. The corresponding geometric variety has dimension 18 and decomposes into $2$ irreducible components determined by the Zariski closures of a two-parameter family of algebras and a four-parameter family of algebras (see Theorem 2). In particular, there are no rigid $4$-dimensional complex nilpotent $\mathfrak{CD}$-algebras.

arXiv admin note: substantial text overlap with arXiv:2001.00253, arXiv:1905.05361; text overlap with arXiv:2006.00734

References in corpus (1)

• Degenerations of Filippov algebras