Some generalizations of the variety of transposed Poisson algebras
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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 Grobner-Shirshov basis for the transposed Poisson operad is calculated up to degree 4. Furthermore, we demonstrate that transposed Poisson algebras are F-manifolds. We verify that the special identities of the variety of GD-algebras hold in transposed Poisson algebras. Finally, we propose a conjecture stating that transposed Poisson algebras are special, i.e., can be embedded into a differential Poisson algebra.Keywords
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