B. K. Sartayev - 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") - https://doi.org/10.46298/cm.11346
Some generalizations of the variety of transposed Poisson algebrasArticle

Authors: 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.

Comment: 8 p, numbers of pages is changed

https://doi.org/10.46298/cm.11346
Source: arXiv.org:2305.12869
Volume: Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
Published on: October 10, 2023
Accepted on: September 20, 2023
Submitted on: May 23, 2023
Keywords: Mathematics - Rings and Algebras
Licence: arXiv.org - Non-exclusive license to distribute

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Mathematics Subject Classification 20201
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  • [1] zbMATH Open.

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