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Representations of finite groups and Cuntz-Krieger algebras. (English) Zbl 0763.22002

Let \(\rho\) be a finite-dimensional representation of a compact group \(G\). The authors shows that each Doplicher-Roberts algebra \({\mathcal O}_ \rho\) [S. Doplicher and J. E. Roberts, J. Funct. Anal. 74, 96-120 (1987; Zbl 0619.46053)] is isomorphic to a corner in the Cuntz-Krieger algebra \({\mathcal O}_ A\) of a \(\{0,1\}\)-matrix \(A=A_ \rho\) associated to \(\rho\).

MSC:

22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
46L80 \(K\)-theory and operator algebras (including cyclic theory)
46L05 General theory of \(C^*\)-algebras
22D35 Duality theorems for locally compact groups

Citations:

Zbl 0619.46053
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References:

[1] Isaacs, Character theory of finite groups (1976) · Zbl 0337.20005
[2] DOI: 10.2307/1971477 · Zbl 0702.46044 · doi:10.2307/1971477
[3] DOI: 10.1007/BF01389192 · Zbl 0461.46047 · doi:10.1007/BF01389192
[4] DOI: 10.1007/BF01390048 · Zbl 0434.46045 · doi:10.1007/BF01390048
[5] DOI: 10.1016/0022-1236(87)90040-1 · Zbl 0619.46053 · doi:10.1016/0022-1236(87)90040-1
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