Some generalizations of the variety of transposed Poisson algebras
Sartayev B.
2024Episciences
Communications in Mathematics
2024#32Issue 257 - 64 pp.
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.
Gelfand-Dorfman algebra , Poisson algebra , Polynomial identities , Transposed Poisson algebra
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SDU University, Kaskelen, Kazakhstan
Kazakhstan and Narxoz University, Almaty, Kazakhstan
SDU University
Kazakhstan and Narxoz University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026