Distributive lattices of varieties of Novikov algebras
arXiv:2406.19319 · doi:10.1007/s00229-025-01629-8
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.
32 pages, comments are welcome