Open Access
2010 Cohomology of Hecke algebras
David Benson, Karin Erdmann, Aram Mikaelian
Homology Homotopy Appl. 12(2): 353-370 (2010).


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.


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David Benson. Karin Erdmann. Aram Mikaelian. "Cohomology of Hecke algebras." Homology Homotopy Appl. 12 (2) 353 - 370, 2010.


Published: 2010
First available in Project Euclid: 28 January 2011

zbMATH: 1236.20002
MathSciNet: MR2771594

Primary: 16A61 , 20C08

Keywords: cohomology ring , Hecke algebra

Rights: Copyright © 2010 International Press of Boston

Vol.12 • No. 2 • 2010
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