The algebraic and geometric classification of nilpotent anticommutative algebras

Kaygorodov, Ivan; Khrypchenko, Mykola; Lopes, Samuel A.

http://hdl.handle.net/10362/148750

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Autores

Kaygorodov, Ivan

Khrypchenko, Mykola

Lopes, Samuel A.

Resumo(s)

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.

Descrição

The first part of this work is supported by the Russian Science Foundation under grant 18-71-10007 . The second part of this work was supported by CNPq 404649/2018-1 ; FAPESP 18/09299-2 , 18/15712-0.