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Representations of finite groups and Cuntz-Krieger algebras

Published online by Cambridge University Press:  17 April 2009

M.H. Mann ,
Iain Raeburn  and
C.E. Sutherland
M.H. Mann
Affiliation:
School of Mathematics University of New South Wales, PO Box 1 Kensington NSW 2033, Australia
Iain Raeburn
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle NSW 2308, Australia
C.E. Sutherland
Affiliation:
School of Mathematics University of New South, Wales PO Box 1 Kensington NSW 2033, Australia
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Abstract

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We investigate the structure of the C*-algebras 𝒪ρ constructed by Doplicher and Roberts from the intertwining operators between the tensor powers of a representation ρ of a compact group. We show that each Doplicher-Roberts algebra is isomorphic to a corner in the Cuntz-Krieger algebra 𝒪A of a {0,1}-matrix A = Aρ associated to ρ. When the group is finite, we can then use Cuntz's calculation of the K-theory of 𝒪A to compute K*(𝒪ρ).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 2 , October 1992 , pp. 225 - 243
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Cuntz, J., ‘A class of C*-algebras and topological Markov chains II: reducible chains and the Ext-functor for C*-algebras’, Invent. Math. 63 (1981), 25–40.CrossRefGoogle Scholar
[2]Cuntz, J. and Krieger, W., ‘A class of C*-algebras and topological Markov chains’, Invent. Math. 56 (1980), 251–268.CrossRefGoogle Scholar
[3]Doplicher, S. and Roberts, J.E., ‘Duals of compact Lie groups realised in the Cuntz algebras and their actions on C*-algebras’, J. Funct. Anal. 74 (1987), 96–120.CrossRefGoogle Scholar
[4]Doplicher, S. and Roberts, J.E., ‘Endomorphisms of C*-algebras, cross products and duality for compact groups’, Ann. of Math. 130 (1989), 75–119.CrossRefGoogle Scholar
[5]Isaacs, I.M., Character theory of finite groups (Academic Press, New York, 1976).Google Scholar
[6]Mann, M.H., Raeburn, I. and Sutherland, C.E., Representations of compact groups, Cuntz-Krieger algebras, and groupoid C*-algebras, Proc. Centre Math. Appl. Austral. Nat. Univ. (to appear).Google Scholar
[7]Shiu, G.Y.-L. and Sutherland, C.E., ‘Groupoid models for AF-algebras’, (submitted).Google Scholar