Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Brauer Group of a Locally Compact Groupoid   We define the Brauer group $\Br(G)$ of a locally compact groupoid $G$ to be
the set of Morita equivalence classes of pairs $(\A,\alpha)$ consisting of an
elementary C*-bundle $\A$ over $G^{(0)}$ satisfying Fell's condition and an
action $\alpha$ of $G$ on $\A$ by $*$-isomorphisms. When $G$ is the
transformation groupoid $X\times H$, then $\Br(G)$ is the equivariant Brauer
group $\Br_H(X)$.
  In addition to proving that $\Br(G)$ is a group, we prove three isomorphism
results. First we show that if $G$ and $H$ are equivalent groupoids, then
$\Br(G)$ and $\Br(H)$ are isomorphic. This generalizes the result that if $G$
and $H$ are groups acting freely and properly on a space $X$, say $G$ on the
left and $H$ on the right then $\Br_G(X/H)$ and $\Br_H(G/ X)$ are isomorphic.
Secondly we show that the subgroup $\Br_0(G)$ of $\Br(G)$ consisting of classes
$[\A,\alpha]$ with $\A$ having trivial Dixmier-Douady invariant is isomorphic
to a quotient $\E(G)$ of the collection $\Tw(G)$ of twists over $G$. Finally we
prove that $\Br(G)$ is isomorphic to the inductive limit $\Ext(G,T)$ of the
groups $\E(G^X)$ where $X$ varies over all principal $G$ spaces $X$ and $G^X$
is the imprimitivity groupoid associated to $X$.

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The categories of this paper are: cs
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The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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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: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph