Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the similarity problem for locally compact quantum groups   A well-known theorem of Day and Dixmier states that any uniformly bounded
representation of an amenable locally compact group $G$ on a Hilbert space is
similar to a unitary representation. Within the category of locally compact
quantum groups, the conjectural analogue of the Day-Dixmier theorem is that
every completely bounded Hilbert space representation of the convolution
algebra of an amenable locally compact quantum group should be similar to a
$\ast$-representation. We prove that this conjecture is false for a large class
of non-Kac type compact quantum groups, including all $q$-deformations of
compact simply connected semisimple Lie groups. On the other hand, within the
Kac framework, we prove that the Day-Dixmier theorem does indeed hold for
several new classes of examples, including amenable discrete quantum groups of
Kac-type.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg