The algebraic and geometric classification of nilpotent anticommutative algebras

Ivan Kaygorodov; Mykola Khrypchenko; Samuel A. Lopes

doi:10.1016/j.jpaa.2020.106337

The algebraic and geometric classification of nilpotent anticommutative algebras

Ivan Kaygorodov, Mykola Khrypchenko, Samuel A. Lopes

CMA - Centro de Matemática e Aplicações

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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.

Original language	English
Article number	106337
Journal	Journal Of Pure And Applied Algebra
Volume	224
Issue number	8
DOIs	https://doi.org/10.1016/j.jpaa.2020.106337
Publication status	Published - Aug 2020

Keywords

Algebraic classification
Anticommutative algebra
Geometric classification
Nilpotent algebra

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10.1016/j.jpaa.2020.106337

1-s2.0-S0022404920300487-mainFinal published version, 389 KBLicence: CC BY-ND

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title = "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.",

keywords = "Algebraic classification, Anticommutative algebra, Geometric classification, Nilpotent algebra",

author = "Ivan Kaygorodov and Mykola Khrypchenko and Lopes, {Samuel A.}",

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doi = "10.1016/j.jpaa.2020.106337",

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AU - Lopes, Samuel A.

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N2 - 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.

AB - 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.

KW - Algebraic classification

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KW - Geometric classification

KW - Nilpotent algebra

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The algebraic and geometric classification of nilpotent anticommutative algebras

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