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On the Dong Property for a binary quadratic operad Научная публикация

Журнал

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Вых. Данные

Год: 2026, Том: 691, Страницы: 428-452 Страниц : 25 DOI: 10.1016/j.jalgebra.2025.11.025

Ключевые слова

Dong lemma Identity; Operad; Manin product

Авторы

Kolesnikov P.S. ¹ , Sartayev B.K. ^2,3

Организации

1	Sobolev Inst Math, Akad Koptyug Prosp 4, Novosibirsk 630090, Russia
2	Narxoz Univ, Zhandossov Str 55, Alma Ata 050035, Kazakhstan
3	SDU Univ, Abylai Khan Str 1-1, Kaskelen 040900, Kazakhstan

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0017

The classical Dong Lemma for distributions over a Lie algebra lies in the foundation of the theory of vertex and conformal algebras. In this paper, we find necessary and sufficient condition for a variety of nonassociative algebras with binary operations to satisfy the analogue of the Dong Lemma. In particular, it turns out that for alternative, Novikov, and Novikov-Poisson algebras the Dong Lemma holds true. The criterion is stated in the language of operads, so we determine for which binary quadratic operads the Dong Lemma holds in the corresponding class of algebras. As an application, we show the black Manin product of such Dong operads is also a Dong operad. (c) 2025 Published by Elsevier Inc.

Kolesnikov P.S. , Sartayev B.K.
On the Dong Property for a binary quadratic operad
Journal of Algebra. 2026. V.691. P.428-452. DOI: 10.1016/j.jalgebra.2025.11.025 WOS

Поступила в редакцию:	18 мар. 2025 г.
Опубликована online:	4 дек. 2025 г.

Web of science:

WOS:001638382400001

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