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arXiv · 2305.12869

Some generalizations of the variety of transposed Poisson algebras

B. K. Sartayev
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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.

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B. K. Sartayev. 2023-05-22. Some generalizations of the variety of transposed Poisson algebras. https://doi.org/10.46298/cm.11346

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