Formal Hecke algebras and algebraic oriented cohomology theories

Cohomology of Hecke Algebras

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.

Equivariant Formal Group Laws and Complex Oriented Cohomology Theories

The article gives an introduction to equivariant formal group laws, and explains its relevance to complex oriented cohomol-ogy theories in general and to complex cobordism in particular.

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...

Hochschild 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...

Cohomology of Algebraic Theories