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1. CJM Online first

Levandovskyy, Viktor; Shepler, Anne V.
Corrigendum to "Quantum Drinfeld Hecke Algebras"
The last example of the article contains an error which we correct. We also indicate some indices in Theorem 11.1 that were accidently transposed.

Keywords:quantum/skew polynomial rings, noncommutative Groebner bases
Categories:16S36, 16S35, 16S80, 16W20, 16Z05, 16E40

2. CJM Online first

Levandovskyy, Viktor; Shepler, Anne V.
Quantum Drinfeld Hecke Algebras
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 PBW conditions.

Keywords:skew polynomial rings, noncommutative Gröbner bases, graded Hecke algebras, symplectic reflection algebras, Hochschild cohomology
Categories:16S36, 16S35, 16S80, 16W20, 16Z05, 16E40

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