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arXiv · 2209.13662

Polynomial identities in Novikov algebras

Vladimir Dotsenko·Nurlan Ismailov·Ualbai Umirbaev
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Abstract

In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity satisfies some unexpected "universal" identities, in particular, right associator nilpotence, and right nilpotence of the commutator ideal. This, in particular, implies that a Novikov algebra over a field of zero characteristic satisfies a nontrivial identity if and only if it is Lie-solvable. We also establish that any system of identities of Novikov algebras over a field of zero characteristic follows from finitely many of them, and that the same holds over any field for multilinear Novikov identities. Some analogous simpler statements are also proved for commutative differential algebras.

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Vladimir Dotsenko, Nurlan Ismailov, Ualbai Umirbaev. 2022-09-27. Polynomial identities in Novikov algebras. https://doi.org/10.1007/s00209-023-03231-8

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