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Auteurs principaux: Kaygorodov, Ivan, Khrypchenko, Mykola, Páez-Guillán, Pilar
Format: Preprint
Publié: 2024
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Accès en ligne:https://arxiv.org/abs/2410.10825
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author Kaygorodov, Ivan
Khrypchenko, Mykola
Páez-Guillán, Pilar
author_facet Kaygorodov, Ivan
Khrypchenko, Mykola
Páez-Guillán, Pilar
contents This is a survey on the geometric classification of different varieties of algebras (nilpotent, nil-, associative, commutative associative, cyclic associative, Jordan, Kokoris, standard, noncommutative Jordan, commutative power-associative, weakly associative, terminal, Lie, Malcev, binary Lie, Tortkara, dual mock Lie, $\mathfrak{CD}$-, commutative $\mathfrak{CD}$-, anticommutative $\mathfrak{CD}$-, symmetric Leibniz, Leibniz, Zinbiel, Novikov, bicommutative, assosymmetric, antiassociative, left-symmetric, right alternative, and right commutative), $n$-ary algebras (Fillipov ($n$-Lie), Lie triple systems and anticommutative ternary), superalgebras (Lie and Jordan), and Poisson-type algebras (Poisson, transposed Poisson, Leibniz-Poisson, generic Poisson, generic Poisson-Jordan, transposed Leibniz-Poisson, Novikov-Poisson, pre-Lie Poisson, commutative pre-Lie, anti-pre-Lie Poisson, pre-Poisson, compatible commutative associative, compatible associative, compatible Novikov, compatible pre-Lie). We also discuss the degeneration level classification.
format Preprint
id arxiv_https___arxiv_org_abs_2410_10825
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The geometric classification of non-associative algebras: a survey
Kaygorodov, Ivan
Khrypchenko, Mykola
Páez-Guillán, Pilar
Rings and Algebras
This is a survey on the geometric classification of different varieties of algebras (nilpotent, nil-, associative, commutative associative, cyclic associative, Jordan, Kokoris, standard, noncommutative Jordan, commutative power-associative, weakly associative, terminal, Lie, Malcev, binary Lie, Tortkara, dual mock Lie, $\mathfrak{CD}$-, commutative $\mathfrak{CD}$-, anticommutative $\mathfrak{CD}$-, symmetric Leibniz, Leibniz, Zinbiel, Novikov, bicommutative, assosymmetric, antiassociative, left-symmetric, right alternative, and right commutative), $n$-ary algebras (Fillipov ($n$-Lie), Lie triple systems and anticommutative ternary), superalgebras (Lie and Jordan), and Poisson-type algebras (Poisson, transposed Poisson, Leibniz-Poisson, generic Poisson, generic Poisson-Jordan, transposed Leibniz-Poisson, Novikov-Poisson, pre-Lie Poisson, commutative pre-Lie, anti-pre-Lie Poisson, pre-Poisson, compatible commutative associative, compatible associative, compatible Novikov, compatible pre-Lie). We also discuss the degeneration level classification.
title The geometric classification of non-associative algebras: a survey
topic Rings and Algebras
url https://arxiv.org/abs/2410.10825