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TitleQuantum Drinfeld Hecke algebras.
Author(s) Viktor Levandovskyy, Anne V. Shepler
TypeArticle in Journal
AbstractWe 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.
Keywordsskew polynomial rings, noncommutative Gröbner bases, graded Hecke algebras, symplectic reflection algebras, Hochschild cohomology
ISSN0008-414X; 1496-4279/e
URL http://cms.math.ca/10.4153/CJM-2013-012-2
JournalCan. J. Math.
PublisherUniversity of Toronto Press, Toronto
Translation No
Refereed No