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Quillen stratification for Hochschild cohomology of blocks
Authors:
Jonathan Pakianathan and Sarah Witherspoon; and with an appendix by Stephen F. Siegel
Journal:
Trans. Amer. Math. Soc. 358 (2006), 2897-2916
MSC (2000):
Primary 20J06
Posted:
December 20, 2005
MathSciNet review:
2216251
Full-text PDF Free Access
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Additional Information
Abstract: We decompose the maximal ideal spectrum of the Hochschild cohomology ring of a block of a finite group into a disjoint union of subvarieties corresponding to elementary abelian  -subgroups of a defect group. These subvarieties are described in terms of group cohomological varieties and the Alperin-Broué correspondence on blocks. Our description leads in particular to a homeomorphism between the Hochschild variety of the principal block and the group cohomological variety. The proofs require a result of Stephen F. Siegel, given in the Appendix, which states that nilpotency in Hochschild cohomology is detected on elementary abelian  -subgroups.
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Additional Information
Jonathan Pakianathan
Affiliation:
Department of Mathematics, University of Rochester, Rochester, New York 14627
Email:
jonpak@math.rochester.edu
Sarah Witherspoon
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email:
sjw@math.tamu.edu
Stephen F. Siegel
Affiliation:
Department of Computer Science, University of Massachusetts, Amherst, Massachusetts 01003-9264
Email:
siegel@cs.umass.edu
DOI:
http://dx.doi.org/10.1090/S0002-9947-05-04012-2
PII:
S 0002-9947(05)04012-2
Received by editor(s):
March 3, 2004
Posted:
December 20, 2005
Additional Notes:
The second author was supported by National Security Agency Grant \#MDS904-01-1-0067 and National Science Foundation Grant \#DMS0245560.
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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