The algebraic and geometric classification of $δ$-Novikov algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914423081271296 |
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| author | Abdelwahab, Hani Kaygorodov, Ivan Lubkov, Roman |
| author_facet | Abdelwahab, Hani Kaygorodov, Ivan Lubkov, Roman |
| contents | The notion of $δ$-Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like $δ$-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras, they have a $2$-dimensional simple algebra for $δ=-1.$ The present paper is dedicated to the study of $3$-dimensional $δ$-Novikov algebras for $δ\notin \big\{0,1\big\}.$ The algebraic and geometric classifications of complex $3$-dimensional $δ$-Novikov algebras are given. As a corollary, we prove that there are no simple $3$-dimensional $δ$-Novikov algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_25079 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The algebraic and geometric classification of $δ$-Novikov algebras Abdelwahab, Hani Kaygorodov, Ivan Lubkov, Roman Rings and Algebras 17A30 (primary), 17D25, 14L30 (secondary) The notion of $δ$-Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like $δ$-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras, they have a $2$-dimensional simple algebra for $δ=-1.$ The present paper is dedicated to the study of $3$-dimensional $δ$-Novikov algebras for $δ\notin \big\{0,1\big\}.$ The algebraic and geometric classifications of complex $3$-dimensional $δ$-Novikov algebras are given. As a corollary, we prove that there are no simple $3$-dimensional $δ$-Novikov algebras. |
| title | The algebraic and geometric classification of $δ$-Novikov algebras |
| topic | Rings and Algebras 17A30 (primary), 17D25, 14L30 (secondary) |
| url | https://arxiv.org/abs/2603.25079 |