Embedding of Novikov algebras into Novikov–Poisson algebras, Witt doubles, isomorphisms of simple Novikov algebras | Sciact - Система учета научной деятельности ИМ СО РАН

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

Журнал

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

Вых. Данные

Год: 2026, Том: 64, Номер: 4, Страницы: 258-274 Страниц : 17 DOI: 10.1007/s10469-026-09831-7

Ключевые слова

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

Авторы

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

Организации

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

Информация о финансировании (1)

Российский научный фонд

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

Поступила в редакцию:	1 окт. 2025 г.
Принята к публикации:	21 янв. 2026 г.
Опубликована online:	12 июн. 2026 г.
Опубликована в печати:	3 сент. 2026 г.

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