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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - B. A. Zambrano
TI  - Poisson brackets on some skew PBW extensions
JO  - Algebra and discrete mathematics
PY  - 2020
SP  - 277
EP  - 302
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a12/
LA  - en
ID  - ADM_2020_29_2_a12
ER  - 
%0 Journal Article
%A B. A. Zambrano
%T Poisson brackets on some skew PBW extensions
%J Algebra and discrete mathematics
%D 2020
%P 277-302
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a12/
%G en
%F ADM_2020_29_2_a12
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/

[1] V. A. Artamonov, “Action of Hopf algebras on General Quantum Malcev power series and Quantum planes”, J. Math. Sci., 134:1 (2006), 1773–1798 | DOI | MR | Zbl

[2] Gallego C. and Lezama O., “Gröbner bases for ideals of sigma-PBW extensions”, Communications in Algebra, 39:1 (2011), 50–75 | DOI | MR | Zbl

[3] Reyes M. A., Ring and Module Theoretic Properties of PBW Extensions, Ph.D. Thesis, Universidad Nacional de Colombia, 2013 | MR

[4] O. Lezama, J. P. Acosta and A. Reyes, “Prime ideals of skew PBW extensions”, Rev. Un. Mat. Argentina, 56:2 (2015), 39–55 | MR | Zbl

[5] O. Lezama and A. Reyes, “Some Homological Properties of Skew PBW Extensions”, Comm. Algebra, 42 (2014), 1200–1230 | DOI | MR | Zbl

[6] A. Reyes and H. Suárez, “Armendariz property for skew PBW extensions and their classical ring of quotients”, Rev. Integr. Temas Mat., 34:2 (2016), 147–168 | DOI | MR | Zbl

[7] Suarez H., “Kozulity for graded skew PBW extensions”, Comm. in Algebra, 45:10 (2017), 4569–4580 | DOI | MR | Zbl

[8] Acosta J. P., Chaparro C., Lezama O., Ojeda I., and Venegas C., “Ore and Goldie theorems for skew PBW extensions”, Asian-European Journal of Mathematics, 6:4 (2013), 1350061-1–1350061-20 | DOI | MR