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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2410.10825 |
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| _version_ | 1866929622463021056 |
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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 |