Cohomology of Hecke Algebras
نویسندگان
چکیده
We compute the cohomology H∗(H, k) = ExtH(k, k) where H = H(n, q) is the Hecke algebra of the symmetric group Sn at a primitive `th root of unity q, and k is a field of characteristic zero. The answer is particularly interesting when ` = 2, which is the only case where it is not graded commutative. We also carry out the corresponding computation for Hecke algebras of type Bn and Dn when ` is odd.
منابع مشابه
Hochschild 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 کاملHochschild 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 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...
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 کاملGerstenhaber Brackets for Skew Group Algebras
Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by automorphisms. We examine the Gerstenhaber bracket with a view toward deformations and developing bracket formulas. We then focus on the linear group actions and p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010