Cohomology of Hecke algebras

David Benson, Karin Erdmann, Aram Mikaelian

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 languageEnglish
Pages (from-to)353-370
Number of pages18
JournalHomology, Homotopy and Applications
Volume12
Issue number2
Publication statusPublished - 2010

Fingerprint

Hecke Algebra
Cohomology
Primitive Roots
Roots of Unity
Symmetric group
Odd
Zero

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.

Cohomology of Hecke algebras. / Benson, David; Erdmann, Karin; Mikaelian, Aram.

In: Homology, Homotopy and Applications, Vol. 12, No. 2, 2010, p. 353-370.

Research output: Contribution to journal › Article

Benson, D, Erdmann, K & Mikaelian, A 2010, 'Cohomology of Hecke algebras', Homology, Homotopy and Applications, vol. 12, no. 2, pp. 353-370.
Benson D, Erdmann K, Mikaelian A. Cohomology of Hecke algebras. Homology, Homotopy and Applications. 2010;12(2):353-370.
Benson, David ; Erdmann, Karin ; Mikaelian, Aram. / Cohomology of Hecke algebras. In: Homology, Homotopy and Applications. 2010 ; Vol. 12, No. 2. pp. 353-370.
@article{623b6d50bbf54324997b4e25492bd20a,
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",
year = "2010",
language = "English",
volume = "12",
pages = "353--370",
journal = "Homology, Homotopy and Applications",
issn = "1532-0073",
publisher = "International Press of Boston, Inc.",
number = "2",

}

TY - JOUR

T1 - Cohomology of Hecke algebras

AU - Benson, David

AU - Erdmann, Karin

AU - Mikaelian, Aram

PY - 2010

Y1 - 2010

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 -

Access to Document