Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of tracial states on reduced group C*-algebras   Let $G$ be a locally compact group. It is not always the case that its
reduced C*-algebra $C^*_r(G)$ admits a tracial state. We exhibit closely
related necessary and sufficient conditions for the existence of such. We gain
a complete answer when $G$ compactly generated. In particular for $G$ almost
connected, or more generally when $C^*_r(G)$ is nuclear, the existence of a
trace is equivalent to amenability. We exhibit two examples of classes of
totally disconnected groups for which $C^*_r(G)$ does not admit a tracial
state.

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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: physics