Hochschild cohomology and quantum Drinfeld Hecke algebras
نویسندگان
چکیده
منابع مشابه
Hochschild Cohomology and Quantum Drinfeld Hecke Algebras
Abstract. Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit connection to Hochschild cohomology. We compute the relevant part of Hochschild cohomology for actions of many reflection groups and we exploit computatio...
متن کاملQuantum 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 proper...
متن کاملHochschild Cohomology and Graded Hecke Algebras
We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V )#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups G(r, p, n) to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give i...
متن کاملHochschild Cohomology and Support Varieties for Tame Hecke Algebras
We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras.
متن کاملOn the Hochschild Cohomology of Tame Hecke Algebras
In this paper we are interested in Hochschild cohomology of finite-dimensional algebras; the main motivation is to generalize group cohomology to larger classes of algebras. If suitable finite generation holds, one can define support varieties of modules as introduced by [SS]. Furthermore, when the algebra is self-injective, many of the properties of group representations generalize to this set...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2016
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-016-0224-3