Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cuntz-Pimsner Algebras of Group Representations   Given a locally compact group $G$ and a unitary representation $\rho:G\to
U({\mathcal H})$ on a Hilbert space ${\mathcal H}$, we construct a
$C^*$-correspondence ${\mathcal E}(\rho)={\mathcal H}\otimes_{\mathbb C}
C^*(G)$ over $C^*(G)$ and study the Cuntz-Pimsner algebra ${\mathcal
O}_{{\mathcal E}(\rho)}$. We prove that for $G$ compact, ${\mathcal
O}_{{\mathcal E}(\rho)}$ is strong Morita equivalent to a graph $C^*$-algebra.
If $\lambda$ is the left regular representation of an infinite, discrete and
amenable group $G$, we show that ${\mathcal O}_{{\mathcal E}(\lambda)}$ is
simple and purely infinite, with the same $K$-theory as $C^*(G)$. If $G$ is
compact abelian, any representation decomposes into characters and determines a
skew product graph. We illustrate with several examples and we compare
${\mathcal E}(\rho)$ with the crossed product $C^*$-correspondence.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas