On the Dong Property for a binary quadratic operad Full article
| Journal |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
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| Output data | Year: 2026, Volume: 691, Pages: 428-452 Pages count : 25 DOI: 10.1016/j.jalgebra.2025.11.025 | ||||||
| Tags | Dong lemma Identity; Operad; Manin product | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0017 |
Abstract:
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.
Cite:
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
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
Dates:
| Submitted: | Mar 18, 2025 |
| Published online: | Dec 4, 2025 |
Identifiers:
| Web of science: | WOS:001638382400001 |
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