Geodesic
Quantum Drinfeld Hecke Algebras
Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 874-901

Voir la notice de l'article provenant de la source Cambridge

DOI

We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the quantum setting over a field of arbitrary characteristic. We give necessary and sufficient conditions for such algebras to satisfy a Poincaré–Birkhoff–Witt property using the theory of noncommutative Gröbner bases. We include applications to the case of abelian groups and the case of groups acting on coordinate rings of quantum planes. In addition, we classify graded automorphisms of the coordinate ring of quantum 3-space. In characteristic zero, Hochschild cohomology gives an elegant description of the Poincaré–Birkhoff–Witt conditions.
DOI : 10.4153/CJM-2013-012-2
Mots-clés : 16S36, 16S35, 16S80, 16W20, 16Z05, 16E40, skew polynomial rings, noncommutative Gröbner bases, graded Hecke algebras, symplectic reflection algebras, Hochschild cohomology 
Levandovskyy, Viktor; Shepler, Anne V. Quantum Drinfeld Hecke Algebras. Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 874-901. doi: 10.4153/CJM-2013-012-2
@article{10_4153_CJM_2013_012_2,
     author = {Levandovskyy, Viktor and Shepler, Anne V.},
     title = {Quantum {Drinfeld} {Hecke} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {874--901},
     year = {2014},
     volume = {66},
     number = {4},
     doi = {10.4153/CJM-2013-012-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-012-2/}
}
TY  - JOUR
AU  - Levandovskyy, Viktor
AU  - Shepler, Anne V.
TI  - Quantum Drinfeld Hecke Algebras
JO  - Canadian journal of mathematics
PY  - 2014
SP  - 874
EP  - 901
VL  - 66
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-012-2/
DO  - 10.4153/CJM-2013-012-2
ID  - 10_4153_CJM_2013_012_2
ER  - 
%0 Journal Article
%A Levandovskyy, Viktor
%A Shepler, Anne V.
%T Quantum Drinfeld Hecke Algebras
%J Canadian journal of mathematics
%D 2014
%P 874-901
%V 66
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-012-2/
%R 10.4153/CJM-2013-012-2
%F 10_4153_CJM_2013_012_2

Cité par Sources :