## Homology, Homotopy and Applications

### Cohomology of Hecke algebras

#### Abstract

We compute the cohomology $H^*(\mathcal{H},k)=\rm{Ext}^*_\mathcal{h}(k,k)$where $\mathcal{H} = \mathcal{H} (n,q)$ is the Hecke algebra of the symmetric group $\mathfrak{S}_n$ at a primitive $\ell$th root of unity $q$, and $k$ is a field of characteristic zero. The answer is particularly interesting when $\ell= 2$, which is the only case where it is not graded commutative. We also carry out the corresponding computation for Hecke algebras of type $B_n$ and $D_n$ when $\ell$ is odd.

#### Article information

Source
Homology Homotopy Appl., Volume 12, Number 2 (2010), 353-370.

Dates
First available in Project Euclid: 28 January 2011

https://projecteuclid.org/euclid.hha/1296223887

Mathematical Reviews number (MathSciNet)
MR2771594

Zentralblatt MATH identifier
1236.20002

Subjects
Primary: 20C08: Hecke algebras and their representations 16A61

Keywords
Hecke algebra cohomology ring

#### Citation

Benson, David; Erdmann, Karin; Mikaelian, Aram. Cohomology of Hecke algebras. Homology Homotopy Appl. 12 (2010), no. 2, 353--370. https://projecteuclid.org/euclid.hha/1296223887