The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

Jumaniyozov Doston; Kaygorodov Ivan; Khudoyberdiyev Abror

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The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

机译：The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

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摘要

We give algebraic and geometric classifications of complex four-dimensional nilpotent noncommutative Jordan algebras. Specifically, we find that, up to isomorphism, there are only 18 non-isomorphic nontrivial nilpotent noncommutative Jordan algebras. The corresponding geometric variety is determined by the Zariski closure of three rigid algebras and two one-parametric families of algebras.

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来源
《Journal of algebra and its applications》 |2021年第11期|共18页
作者
Jumaniyozov Doston; Kaygorodov Ivan; Khudoyberdiyev Abror;
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作者单位

Natl Univ Uzbekistan;

Fed Univ ABC;

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原文格式 PDF
正文语种英语
中图分类代数、数论、组合理论;
关键词
Noncommutative Jordan algebras; nilpotent algebras; algebraic classification; central extension; geometric classification; degeneration; LIE-ALGEBRAS; CENTRAL EXTENSIONS; DEGENERATIONS; REPRESENTATIONS; VARIETIES; FIELDS;

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The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

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