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Algebraic and geometric classification of nilpotent anticommutative algebras

Preprint

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.

Ivan Kaygorodov

Mykola Khrypchenko

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Year of publication: 2019

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Preprint

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