Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Baum--Connes conjecture for discrete quantum groups with torsion
  and the quantum Rosenberg Conjecture   We give a decomposition of the equivariant Kasparov category for discrete
quantum group with torsions. As an outcome, we show that the crossed product by
a discrete quantum group in a certain class preserves the UCT. We then show
that quasidiagonality of a reduced C*-algebra of a countable discrete quantum
group $\Gamma$ implies that $\Gamma$ is amenable, and deduce from the work of
Tikuisis, White and Winter, and the results in the first part of the paper, the
converse (i.e. the quantum Rosenberg Conjecture) for a large class of countable
discrete unimodular quantum groups. We also note that the unimodularity is a
necessary condition.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph