Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs of quantum groups and K-amenability   Building on a construction of J-P. Serre, we associate to any graph of
C*-algebras a maximal and a reduced fundamental C*-algebra and use this theory
to construct the fundamental quantum group of a graph of discrete quantum
groups. This construction naturally gives rise to a quantum Bass-Serre tree
which can be used to study the K-theory of the fundamental quantum group. To
illustrate the properties of this construction, we prove that if all the vertex
qantum groups are amenable, then the fundamental quantum group is K-amenable.
This generalizes previous results of P. Julg, A. Valette, R. Vergnioux and the
first author.

20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat