Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely bounded representations of convolution algebras of locally
  compact quantum groups   Given a locally compact quantum group $\mathbb G$, we study the structure of
completely bounded homomorphisms $\pi:L^1(\mathbb G)\rightarrow\mathcal B(H)$,
and the question of when they are similar to $\ast$-homomorphisms. By analogy
with the cocommutative case (representations of the Fourier algebra $A(G)$), we
are led to consider the associated map $\pi^*:L^1_\sharp(\mathbb G) \rightarrow
\mathcal B(H)$ given by $\pi^*(\omega) = \pi(\omega^\sharp)^*$. We show that
the corepresentation $V_\pi$ of $L^\infty(\mathbb G)$ associated to $\pi$ is
invertible if and only if both $\pi$ and $\pi^*$ are completely bounded.
Moreover, we show that the co-efficient operators of such representations give
rise to completely bounded multipliers of the dual convolution algebra
$L^1(\hat \mathbb G)$. An application of these results is that any
(co)isometric corepresentation is automatically unitary. An averaging argument
then shows that when $\mathbb G$ is amenable, $\pi$ is similar to a
*-homomorphism if and only if $\pi^*$ is completely bounded. For compact Kac
algebras, and for certain cases of $A(G)$, we show that any completely bounded
homomorphism $\pi$ is similar to a *-homomorphism, without further assumption
on $\pi^*$. Using free product techniques, we construct new examples of compact
quantum groups $\mathbb G$ such that $L^1(\mathbb G)$ admits bounded, but not
completely bounded, representations.

9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph