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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2023 Volume 64, Number 3, Pages 546–561 (Mi smj7780)

Conformal envelopes of Novikov–Poisson algebras

P. S. Kolesnikova, A. A. Nesterenkob

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: We prove that every Novikov–Poisson algebra over a field of zero characteristic can be embedded into a commutative conformal algebra with a derivation. As a corollary, we show that every commutator Gelfand–Dorfman algebra obtained from a Novikov–Poisson algebra is special, i.e., embeddable into a differential Poisson algebra.

Keywords: Novikov–Poisson algebra, conformal algebra, Gelfand–Dorfman algebra, Poisson algebra.

UDC: 512.554

Received: 03.02.2023
Revised: 03.02.2023
Accepted: 06.04.2023

DOI: 10.33048/smzh.2023.64.308



© Steklov Math. Inst. of RAS, 2024