Author:
Kolesnikov P. S.,Nesterenko A. A.
Abstract
AbstractWe 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.
Reference19 articles.
1. Gelfand I.M. and Dorfman I.Ya., “Hamiltonian operators and algebraic structures related to them,” Funct. Anal. Appl., vol. 13, no. 4, 248–262 (1979).
2. Balinskii A.A. and Novikov S.P., “Poisson brackets of hydrodynamic type, Frobenius algebras, and Lie algebras,” Soviet Math. Dokl., vol. 32, no. 1, 228–231 (1985).
3. Xu X., “Novikov–Poisson algebras,” J. Algebra, vol. 190, 253–279 (1997).
4. Zhelyabin V.N. and Tikhov A.S., “Novikov–Poisson algebras and associative commutative derivation algebras,” Algebra Logic, vol. 47, no. 2, 107–117 (2008).
5. Zakharov A.S., “Gelfand–Dorfman–Novikov–Poisson superalgebras and their envelopes,” Sib. Electr. Math. Reports, vol. 16, 1843–1855 (2019).
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1. Transposed Poisson Structures;Results in Mathematics;2024-02-10