B. K. Sartayev
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Some generalizations of the variety of transposed Poisson algebras
cm:11346 -
Communications in Mathematics,
October 10, 2023,
Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
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https://doi.org/10.46298/cm.11346
Some generalizations of the variety of transposed Poisson algebrasArticle
Authors: B. K. Sartayev
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B. K. Sartayev
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.