Geodesic
Poisson brackets on some skew PBW extensions
Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 277-302

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In [1] the author gives a description of Poisson brackets on some algebras of quantum polynomials $\mathcal{O}_q$, which is called the general algebra of quantum polynomials. The main of this paper is to present a generalization of [1] through a description of Poisson brackets on some skew PBW extensions of a ring $A$ by the extensions $\mathcal{O}_{q,\delta}^{r,n}$, which are generalization of $\mathcal{O}_q$, and show some examples of skew PBW extension where we can apply this description.
Keywords: noncommutative rings, skew PBW extensions.
Mots-clés : Poisson brackets 
@article{ADM_2020_29_2_a12,
     author = {B. A. Zambrano},
     title = {Poisson brackets on some skew {PBW} extensions},
     journal = {Algebra and discrete mathematics},
     pages = {277--302},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a12/}
}
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B. A. Zambrano. Poisson brackets on some skew PBW extensions. Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 277-302. http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a12/