Details:
Title  Quantum Drinfeld Hecke algebras.  Author(s)  Viktor Levandovskyy, Anne V. Shepler  Type  Article in Journal  Abstract  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 PoincaréBirkhoffWitt 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 3space. In characteristic zero, Hochschild cohomology gives an elegant description of the PBW conditions.  Keywords  skew polynomial rings, noncommutative Gröbner bases, graded Hecke algebras, symplectic reflection algebras, Hochschild cohomology  ISSN  0008414X; 14964279/e 
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 URL 
http://cms.math.ca/10.4153/CJM20130122 
Language  English  Journal  Can. J. Math.  Volume  66  Number  4  Pages  874901  Publisher  University of Toronto Press, Toronto  Year  2014  Edition  0  Translation 
No  Refereed 
No 
