Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K-theory for the tame C*-algebra of a separated graph   A {\it separated graph} is a pair $(E,C)$ consisting of a directed graph $E$
and a set $C=\bigsqcup_{v\in E^0}C_v$, where each $C_v$ is a partition of the
set of edges whose terminal vertex is $v$. Given a separated graph $(E,C)$,
such that all the sets $X\in C$ are finite, the K-theory of the graph
C*-algebra $C^*(E,C)$ is known to be determined by the kernel and the cokernel
of a certain map, denoted by $1_C- A_{(E,C)}$, from $\mathbb Z^{(C)}$ to
$\mathbb Z^{(E^0)}$. In this paper, we compute the K-theory of the {\it tame}
graph C*-algebra $\mathcal O(E,C)$ associated to $(E,C)$, which has been
recently introduced by the authors. Letting $\pi$ denote the natural surjective
homomorphism from $C^*(E,C)$ onto $\mathcal O(E,C)$, we show that $K_1(\pi)$ is
a group isomorphism, and that $K_0(\pi)$ is a split monomorphism, whose
cokernel is a torsion-free abelian group. We also prove that this cokernel is a
free abelian group when the graph $E$ is finite, and determine its generators
in terms of a sequence of separated graphs $\{(E_n, C^n)\}_{n=1}^{\infty}$
naturally attached to $(E,C)$. On the way to showing our main results, we
obtain an explicit description of a connecting map arising in a six-term exact
sequence computing the K-theory of an amalgamated free product, and we also
exhibit an explicit isomorphism between $\mathrm{ker} (1_C - A_{(E,C)})$ and
$K_1(C^*(E,C))$.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn