Embedding of Novikov algebras into Novikov–Poisson algebras, Witt doubles, isomorphisms of simple Novikov algebras

Embedding of Novikov algebras into Novikov–Poisson algebras, Witt doubles, isomorphisms of simple Novikov algebras Full article

Journal

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Output data

Year: 2026, Volume: 64, Number: 4, Pages: 258-274 Pages count : 17 DOI: 10.1007/s10469-026-09831-7

Tags

left-symmetric algebra, pre-Lie algebra, Novikov algebra, Novikov–Poisson algebra, simple algebra, Gelfand–Dorfman construction, isomorphism.

Authors

Pozhidaev A.P. ¹ , Zhelyabin V.N. ¹ , Zaharov A.S. ^1,2

Affiliations

1	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
2	Novosibirsk State Technical University, Novosibirsk, Russia

Funding (1)

Russian Science Foundation

25-41-00005

We prove that every nonassociative Novikov algebra can be equipped with a nontrivial structure of a Novikov–Poisson algebra. Using this result, we show that, under certain finiteness conditions, every simple Novikov algebra is obtained by the Gelfand–Dorfman construction applied to an associative commutative differentially simple algebra. We also introduce and study the Witt doubles of Novikov–Poisson algebras. The description of the isomorphisms of simple Novikov algebras over an algebraically closed field is reduced to the description of some special automorphisms of the underlying associative commutative algebras.

Pozhidaev A.P. , Zhelyabin V.N. , Zaharov A.S.
Embedding of Novikov algebras into Novikov–Poisson algebras, Witt doubles, isomorphisms of simple Novikov algebras
Algebra and Logic. 2026. V.64. N4. P.258-274. DOI: 10.1007/s10469-026-09831-7

Submitted:	Oct 1, 2025
Accepted:	Jan 21, 2026
Published online:	Jun 12, 2026
Published print:	Sep 3, 2026

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