The algebraic and geometric classification of nilpotent anticommutative algebras

Abstract

We give algebraic and geometric classifications of $6$-dimensional complex nilpotent anticommutative algebras. Specifically, we find that, up to isomorphism, there are $14$ one-parameter families of $6$-dimensional nilpotent anticommutative algebras, complemented by $130$ additional isomorphism classes. The corresponding geometric variety is irreducible and determined by the Zariski closure of a one-parameter family of algebras. In particular, there are no rigid $6$-dimensional complex nilpotent anticommutative algebras.

arXiv admin note: text overlap with arXiv:1905.05361; text overlap with arXiv:1912.02691 by other authors