Some generalizations of the variety of transposed Poisson algebras

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 Gröbner-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.

8 p, numbers of pages is changed

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• The algebraic and geometric classification of transposed Poisson algebras
• Transposed Poisson structures on Galilean and solvable Lie algebras
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Cited by in corpus (2)

• Transposed Poisson structures on the Lie algebra of upper triangular matrices
• Quantizations of transposed Poisson algebras by Novikov deformations