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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

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