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Algebraic Constructions for Novikov–Poisson Algebras

Mathematics, 2022
A Novikov–Poisson algebra (A,∘,·) is a vector space with a Novikov algebra structure (A,∘) and a commutative associative algebra structure (A,·) satisfying some compatibility conditions. Give a Novikov–Poisson algebra (A,∘,·) and a vector space V.
Naping Bao, Yanyong Hong
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Poisson C*-algebra derivations in Poisson C*-algebras

Demonstratio Mathematica
In this study, we introduce the following additive functional equation:g(λu+v+2y)=λg(u)+g(v)+2g(y)g\left(\lambda u+v+2y)=\lambda g\left(u)+g\left(v)+2g(y) for all λ∈C\lambda \in {\mathbb{C}}, all unitary elements u,vu,v in a unital Poisson C*{C ...
Wang Yongqiao, Park Choonkil, Chang Yuan
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On the Kantor product, II

Karpatsʹkì Matematičnì Publìkacìï, 2022
We describe the Kantor square (and Kantor product) of multiplications, extending the classification proposed in [J. Algebra Appl. 2017, 16 (9), 1750167].
R. Fehlberg Júnior, I. Kaygorodov
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On analogs of some classical group-theoretic results in Poisson algebras

Доповiдi Нацiональної академiї наук України, 2021
We investigate the Poisson algebras, in which the n-th hypercenter (center) has a finite codimension. It was established that, in this case, the Poisson algebra P includes a finite-dimensional ideal K such that P/K is nilpotent (Abelian).
L.A. Kurdachenko, A.A. Pypka, I.Ya. Subbotin   +2 more
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Poisson gauge theory

Journal of High Energy Physics, 2021
The Poisson gauge algebra is a semi-classical limit of complete non- commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a corresponding ...
Vladislav G. Kupriyanov
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Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras

Journal of Algebra, 2023
We introduce a dual notion of the Poisson algebra by exchanging the roles of the two binary operations in the Leibniz rule defining the Poisson algebra. We show that the transposed Poisson algebra thus defined not only shares common properties of the Poisson algebra, including the closure under taking tensor products and the Koszul self-duality as an ...
Chengming Bai, Ruipu Bai, Li Guo, Yong Wu   +3 more
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Cyclic $A_\infty$-algebras and double Poisson algebras [PDF]

Journal of Noncommutative Geometry, 2021
In this article we prove that there exists an explicit bijection between nice d -pre-Calabi–Yau algebras and d -double Poisson differential graded algebras, where
David Fernández, Estanislao Herscovich
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Restricted Poisson algebras [PDF]

Pacific Journal of Mathematics, 2017
We re-formulate Bezrukavnikov-Kaledin's definition of a restricted Poisson algebra, provide some natural and interesting examples, and discuss connections with other research topics.
Bao, Yan-Hong, Ye, Yu, Zhang, James
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Category of quantizations and inverse problem

Nuclear Physics B, 2023
We introduce a category composed of all quantizations of all Poisson algebras. By the category, we can treat in a unified way the various quantizations for all Poisson algebras and develop a new classical limit formulation.
Akifumi Sako
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A new integrable structure associated to the Camassa-Holm peakons

SciPost Physics, 2023
We provide a closed Poisson algebra involving the Ragnisco-Bruschi generalization of peakon dynamics in the Camassa-Holm shallow-water equation. This algebra is generated by three independent matrices.
Jean Avan, Luc Frappat, Eric Ragoucy
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