On the generalized Poisson and transposed Poisson algebras
Dzhumadil’Daev A. Ismailov N. Mashurov F.
2025World Scientific
Journal of Algebra and its Applications
2025
We provide the polynomial identities of algebras that are both generalized Poisson algebras and transposed Poisson algebras. We establish defining identities via single operation for generalized Poisson algebras and prove that Itô’s theorem holds for generalized Poisson algebras.
Generalized Poisson algebra , polynomial identities , transposed Poisson algebra
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Astana IT University, Astana, 020000, Kazakhstan
SDU University, Shenzhen International Center for Mathematics, Southern University of Science and Technology, Kaskelen, Kazakhstan
Shenzhen International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China
Institute of Mathematics and Mathematical Modeling
Astana IT University
SDU University
Shenzhen International Center for Mathematics
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