Distributive lattices of varieties of Novikov algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914850668544000 |
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| author | Dotsenko, Vladimir Zhakhayev, Bekzat |
| author_facet | Dotsenko, Vladimir Zhakhayev, Bekzat |
| contents | We prove that a variety of Novikov algebras has a distributive lattice of subvarieties if and only if the lattice of its subvarieties defined by identities of degree three is distributive, thus answering, in the case of Novikov algebras, a question of Bokut from about fifty years ago. As a byproduct, we classify all Koszul operads with one binary generator of which the Novikov operad is a quotient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributive lattices of varieties of Novikov algebras Dotsenko, Vladimir Zhakhayev, Bekzat Rings and Algebras Category Theory We prove that a variety of Novikov algebras has a distributive lattice of subvarieties if and only if the lattice of its subvarieties defined by identities of degree three is distributive, thus answering, in the case of Novikov algebras, a question of Bokut from about fifty years ago. As a byproduct, we classify all Koszul operads with one binary generator of which the Novikov operad is a quotient. |
| title | Distributive lattices of varieties of Novikov algebras |
| topic | Rings and Algebras Category Theory |
| url | https://arxiv.org/abs/2406.19319 |