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arXiv · 2406.19319

Distributive lattices of varieties of Novikov algebras

Vladimir Dotsenko·Bekzat Zhakhayev
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Abstract

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.

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Vladimir Dotsenko, Bekzat Zhakhayev. 2024-06-27. Distributive lattices of varieties of Novikov algebras. https://doi.org/10.1007/s00229-025-01629-8

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