Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dixmier-Douady Classes of Certain Groupoid $C^*$-Algebras with
  Continuous Trace   Given a locally compact abelian group $G$, we give an explicit formula for
the Dixmier--Douady invariant of the $C^*$-algebra of the groupoid extension
associated to a \v{C}ech $2$-cocycle in the sheaf of germs of continuous
$G$-valued functions. We then exploit the blow-up construction for groupoids to
extend this to some more general central extensions of \'etale equivalence
relations.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys