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Non-Commutative Ternary Nambu-Poisson Algebras and Ternary Hom-Nambu-Poisson Algebras [PDF]
Journal of Generalized Lie Theory and Applications, 2015 The main purpose of this paper is to study non-commutative ternary Nambu-Poisson algebras and their Hom-type version. We provide construction results dealing with tensor product and direct sums of two (non-commutative) ternary (Hom-)Nambu-Poisson algebras. Moreover, we explore twisting principle of (non-commutative) ternary Nambu-Poisson algebras along
Amri, Hanene, Makhlouf, Abdenacer
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The automorphism group of Poisson algebras on k[x; y]
Қарағанды университетінің хабаршысы. Математика сериясы, 2017 Poisson algebras play a key role in the Hamiltonian mechanics, symplectic geometry and also are central in the study of quantum groups. At present, Poisson algebras are investigated by the many mathematicians of Russia, France, the USA, Brazil ...
U. Turusbekova, G. Azieva
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Hall algebras as Poisson algebras [PDF]
SCIENTIA SINICA Mathematica, 2018 Motivated by Joyces work on motivic Hall algebras, we observe that for an algebra $\Lambda$ with Hall polynomials,the Hall algebra $\mathcal{H}(\Lambda)$ of $\Lambda$ admits a natural structure of Poisson algebra. For a given antisymmetric bilinear form over its Grothendieck group $\go(\Lambda)$satisfying certain condition, there is a homomorphism of ...
Fu Changjian, Peng Lian'gang
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Transactions of the American Mathematical Society, 2007 We study Poisson algebras satisfying polynomial identities. In particular, such algebras satisfy “customary” identities (Farkas, 1998, 1999) Our main result is that the growth of the corresponding codimensions of a Poisson algebra with a nontrivial identity is exponential, with an integer exponent.
Mishchenko, S. P. +2 more
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VERTEX ALGEBRAS AND VERTEX POISSON ALGEBRAS [PDF]
Communications in Contemporary Mathematics, 2004 This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general construction theorems of vertex Poisson algebras are given.
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Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators
Topological Algebra and its Applications, 2018 We study algebraic properties of Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Special attention is paid to the Poisson brackets of the Lie-Poisson type, related with the special Lie ...
Artemovych Orest D. +2 more
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On Leibniz-Poisson special polynomial identities
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 In this paper we study Leibniz-Poisson algebras satisfying polynomial identities. We study Leibniz-Poisson special and Leibniz-Poisson extended special polynomials.
Sergey M Ratseev, Olga I Cherevatenko
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On the Heisenberg invariance and the Elliptic Poisson tensors [PDF]
, 2010 We study different algebraic and geometric properties of Heisenberg invariant Poisson polynomial quadratic algebras. We show that these algebras are unimodular.
A. Lichnerowicz +27 more
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Poisson catenarity in Poisson nilpotent algebras
Journal of Algebra, 2022 We prove that for the iterated Poisson polynomial rings known as Poisson nilpotent algebras (or Poisson-CGL extensions), the Poisson prime spectrum is catenary, i.e., all saturated chains of inclusions of Poisson prime ideals between any two given Poisson prime ideals have the same length.
Goodearl, K. R., Launois, S.
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Normalization of a Poisson algebra is Poisson [PDF]
Proceedings of the Steklov Institute of Mathematics, 2009 We prove that the integral closure of a Poisson algebra $A$ over a field of characteristic 0 is again a Poisson algebra.
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