Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Connes embedding property for quantum group von Neumann algebras   For a compact quantum group $\mathbb G$ of Kac type, we study the existence
of a Haar trace-preserving embedding of the von Neumann algebra
$L^\infty(\mathbb G)$ into an ultrapower of the hyperfinite II$_1$-factor (the
Connes embedding property for $L^\infty(\mathbb G)$). We establish a connection
between the Connes embedding property for $L^\infty(\mathbb G)$ and the
structure of certain quantum subgroups of $\mathbb G$, and use this to prove
that the II$_1$-factors $L^\infty(O_N^+)$ and $L^\infty(U_N^+)$ associated to
the free orthogonal and free unitary quantum groups have the Connes embedding
property for all $N \ge 4$. As an application, we deduce that the free entropy
dimension of the standard generators of $L^\infty(O_N^+)$ equals $1$ for all $N
\ge 4$. We also mention an application of our work to the problem of
classifying the quantum subgroups of $O_N^+$.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an