Poisson structures on (non)associative noncommutative algebras and integrable Kontsevich type Hamiltonian systems

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Oksana E Hentosh*
Alexander A Balinsky
Anatolij K Prykarpatski*

Abstract

We have revisited the classical Poisson manifold approach, closely related to construction of Hamiltonian operators, generated by nonassociative and noncommutative algebras. In particular, we presented its natural and simple generalization allowing effectively to describe a wide class of Lax type integrable nonlinear Kontsevich type Hamiltonian systems on associative noncommutative algebras.

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Hentosh, O. E., Balinsky, A. A., & Prykarpatski, A. K. (2020). Poisson structures on (non)associative noncommutative algebras and integrable Kontsevich type Hamiltonian systems. Annals of Mathematics and Physics, 3(1), 001–006. https://doi.org/10.17352/amp.000010
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Copyright (c) 2020 Hentosh OE, et al.

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