Cohomology of Hecke algebras

David Benson; Karin Erdmann; Aram Mikaelian

Cohomology of Hecke algebras

David Benson, Karin Erdmann, Aram Mikaelian

Mathematical Science

Research output: Contribution to journal › Article

Abstract

We compute the cohomology H*(H,k)=Ext*H(k,k) where H=H(n,q) is the Hecke algebra of the symmetric group Sn at a primitive lth root of unity q, and k is a field of characteristic zero. The answer is particularly interesting when l = 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 l is odd.

Original language	English
Pages (from-to)	353-370
Number of pages	18
Journal	Homology, Homotopy and Applications
Volume	12
Issue number	2
Publication status	Published - 2010

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Keywords

Hecke algebra
cohomology ring

Cite this

Benson, D., Erdmann, K., & Mikaelian, A. (2010). Cohomology of Hecke algebras. Homology, Homotopy and Applications, 12(2), 353-370. http://projecteuclid.org/euclid.hha/1296223887

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title = "Cohomology of Hecke algebras",

abstract = "We compute the cohomology H*(H,k)=Ext*H(k,k) where H=H(n,q) is the Hecke algebra of the symmetric group Sn at a primitive lth root of unity q, and k is a field of characteristic zero. The answer is particularly interesting when l = 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 l is odd.",

keywords = "Hecke algebra, cohomology ring",

author = "David Benson and Karin Erdmann and Aram Mikaelian",

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pages = "353--370",

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T1 - Cohomology of Hecke algebras

AU - Benson, David

AU - Erdmann, Karin

AU - Mikaelian, Aram

PY - 2010

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N2 - We compute the cohomology H*(H,k)=Ext*H(k,k) where H=H(n,q) is the Hecke algebra of the symmetric group Sn at a primitive lth root of unity q, and k is a field of characteristic zero. The answer is particularly interesting when l = 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 l is odd.

AB - We compute the cohomology H*(H,k)=Ext*H(k,k) where H=H(n,q) is the Hecke algebra of the symmetric group Sn at a primitive lth root of unity q, and k is a field of characteristic zero. The answer is particularly interesting when l = 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 l is odd.

KW - Hecke algebra

KW - cohomology ring

M3 - Article

VL - 12

SP - 353

EP - 370

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

SN - 1532-0073

IS - 2

ER -

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