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arXiv · 2001.00253

The algebraic and geometric classification of nilpotent anticommutative algebras

Ivan Kaygorodov·Mykola Khrypchenko·Samuel A. Lopes
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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.

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Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes. 2020-01-01. The algebraic and geometric classification of nilpotent anticommutative algebras. https://doi.org/10.1016/j.jpaa.2020.106337

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