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The Hochschild cohomology ring of a cyclic block
Author(s):
Stephen
F.
Siegel;
Sarah
J.
Witherspoon
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1263-1268.
MSC (2000):
Primary 20J06, 16E40
Posted:
February 7, 2000
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Abstract:
Suppose  is a block of a group algebra  with cyclic defect group. We calculate the Hochschild cohomology ring of  , giving a complete set of generators and relations. We then show that if  is the principal block, the canonical map from  to the Hochschild cohomology ring of  induces an isomorphism modulo radicals.
References:
-
- 1.
- J. L. Alperin, Local Representation Theory, Cambridge University Press, 1986. MR 87i:20002
- 2.
- C. Cibils and A. Solotar, Hochschild cohomology algebra of abelian groups, Arch. Math. 68 (1997), 17-21. MR 97k:13018
- 3.
- C. W. Curtis and I. Reiner, Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II, Wiley, 1987. MR 88f:20002
- 4.
- K. Erdmann and T. Holm, Twisted bimodules and Hochschild cohomology for self-injective algebras of class
 , Forum Math. 11 (1999), 177-201. CMP 99:11 - 5.
- L. Evens, Cohomology of Groups, Oxford University Press, 1991. MR 93i:20059
- 6.
- T. Holm, The even Hochschild cohomology ring of a block with cyclic defect group, J. Alg. 178 (1995) 317-341. MR 96m:16014
- 7.
- J. Rickard, Derived categories and stable equivalence, J. Pure and App. Alg. 61 (1989), 303-317. MR 91a:16004
- 8.
- J. Rickard, Derived equivalences as derived functors, J. London Math. Soc. 43 (1991), 37-48. MR 92b:16043
- 9.
- R. Rouquier, From stable equivalences to Rickard equivalences for blocks with cyclic defect, Groups '93 Galway/St. Andrews, Vol. 2, 512-523, London Math. Soc. Lecture Note Ser., 212, Cambridge University Press, 1995. MR 96h:20021
- 10.
- S. F. Siegel and S. J. Witherspoon, The Hochschild cohomology ring of a group algebra, Proc. London Math. Soc. (3) 79 (1999), 131-157. MR 2000b:16016
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Additional Information:
Stephen
F.
Siegel
Affiliation:
Department of Computer Science, University of Massachusetts, Amherst, Massachusetts 01003-4610
Email:
siegel@cs.umass.edu
Sarah
J.
Witherspoon
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
withersp@math.wisc.edu
DOI:
10.1090/S0002-9939-00-05466-6
PII:
S 0002-9939(00)05466-6
Keywords:
Finite groups,
representation theory,
Hochschild cohomology,
blocks,
cyclic defect
Received by editor(s):
March 15, 1998
Posted:
February 7, 2000
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
2000,
American Mathematical Society
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