Some generalizations of the variety of transposed Poisson algebras
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Open Access
- 10 October 2023
- journal article
- research article
- Published by Centre pour la Communication Scientifique Directe (CCSD) in Communications in Mathematics
- Vol. ume 32 (20
Abstract
It is shown that the variety of transposed Poisson algebras coincides with the variety of Gelfand-Dorfman algebras in which the Novikov multiplication is commutative. The Gr\"obner-Shirshov basis for the transposed Poisson operad is calculated up to degree 4. Furthermore, we demonstrate that every transposed Poisson algebra is F-manifold. We verify that the special identities of GD-algebras hold in transposed Poisson algebras. Finally, we propose a conjecture stating that every transposed Poisson algebra is special, i.e., can be embedded into a differential Poisson algebra.Keywords
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