Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Hausdorff etale groupoids and C*-algebras of left cancellative
  monoids   We study the question whether the representations defined by a dense subset
of the unit space of a locally compact \'etale groupoid are enough to determine
the reduced norm on the groupoid C$^*$-algebra. We present sufficient
conditions for either conclusion, giving a complete answer when the isotropy
groups are torsion-free. As an application we consider the groupoid $G(S)$
associated to a left cancellative monoid $S$ by Spielberg and formulate a
sufficient condition, which we call C$^*$-regularity, for the canonical map
$C^*_r(G(S))\to C^*_r(S)$ to be an isomorphism, in which case $S$ has a
well-defined full semigroup C$^*$-algebra $C^*(S)=C^*(G(S))$. We give two
related examples of left cancellative monoids $S$ and $T$ such that both are
not finitely aligned and have non-Hausdorff associated \'etale groupoids, but
$S$ is C$^*$-regular, while $T$ is not.

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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat