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Hecke algebras of semidirect products
Author(s):
Marcelo
Laca;
Nadia
S.
Larsen
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2189-2199.
MSC (2000):
Primary 46L55
Posted:
November 13, 2002
Errata:
Proc. Amer. Math. Soc. 133 (2005), 1255-1256.
MathSciNet review:
1963767
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Abstract:
We consider group-subgroup pairs in which the group is a semidirect product and the subgroup is contained in the normal part. We give conditions for the pair to be a Hecke pair and we show that the enveloping Hecke algebra and Hecke  -algebra are canonically isomorphic to semigroup crossed products, generalizing earlier results of Arledge, Laca and Raeburn and of Brenken.
References:
-
- 1.
- J. Arledge, M. Laca and I. Raeburn, Semigroup crossed products and Hecke algebras arising from number fields, Documenta Math. 2 (1997), 115-138. MR 98k:46111
- 2.
- M. W. Binder, Induced factor representations of discrete groups and their types, J. Funct. Anal. 115 (1993), 294-312. MR 94g:22010
- 3.
- B. Blackadar, Shape theory for
 -algebras, Math. Scand. 56 (1985), 249-275. MR 87b:46074 - 4.
- J.-B. Bost and A. Connes, Hecke algebras, Type III factors and phase transitions with spontaneous symmetry breaking in number theory, Selecta Math. (New Series) 1 (1995), 411-457. MR 96m:46112
- 5.
- B. Brenken, Hecke algebras and semigroup crossed product
 -algebras, Pacific J. Math. 187 (1999), 241-262. MR 2000g:46071 - 6.
- R. W. Hall, Hecke
 -algebras, Ph.D. thesis, The Pennsylvania State University, December 1999. - 7.
- A. Krieg, Hecke Algebras, Mem. Amer. Math. Soc. 87 (1990), No. 435. MR 90m:16024
- 8.
- M. Laca and I. Raeburn, Semigroup crossed products and the Toeplitz algebras of nonabelian groups, J. Funct. Anal. 139 (1996), 415-440. MR 97h:46109
- 9.
- M. Laca and I. Raeburn, A semigroup crossed product arising in number theory, J. London Math. Soc. 59 (1999), 330-344. MR 2000g:46097
- 10.
- M. Laca and I. Raeburn, The ideal structure of the Hecke
 -algebra of Bost and Connes, Math. Ann. 318 (2000), 433-451. MR 2002a:46095 - 11.
- M. Laca, From endomorphisms to automorphisms and back: dilations and full corners, J. London Math. Soc. (2) 61 (2000), 893-904. MR 2002a:46094
- 12.
- M. Laca, M. van Frankenhuysen, Phase transitions on Hecke C*-algebras and class field theory, in preparation.
- 13.
- N. S. Larsen and I. Raeburn, Faithful representations of crossed products by actions of
 , Math. Scand. 89 (2001), 283-296. - 14.
- N. S. Larsen and I. Raeburn, Representations of Hecke algebras and dilations of semigroup crossed products, J. London Math. Soc., to appear.
- 15.
- G. J. Murphy, Crossed products of
 -algebras by endomorphisms, Integral Equations & Operator Theory 24 (1996), 298-319. MR 97f:46105 - 16.
- K. Tzanev, C*-algèbres de Hecke et K-theorie, Thèse de Doctorat, Université de Paris 7, December 2000.
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Additional Information:
Marcelo
Laca
Affiliation:
Department of Mathematics, University of Münster, 48149 Münster, Germany
Address at time of publication:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4
Email:
laca@math.uni-muenster.de
Nadia
S.
Larsen
Affiliation:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
Email:
nadia@math.ku.dk
DOI:
10.1090/S0002-9939-02-06851-X
PII:
S 0002-9939(02)06851-X
Received by editor(s):
July 15, 2001
Received by editor(s) in revised form:
January 22, 2002 and March 5, 2002
Posted:
November 13, 2002
Additional Notes:
The first author was supported by the Deutsche Forschungsgemeinschaft [SFB 478]
The second author was supported by the Danish Natural Science Research Council and The Carlsberg Foundation
Communicated by:
David R. Larson
Copyright of article:
Copyright
2002,
American Mathematical Society
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