Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical systems associated to separated graphs, graph algebras, and
  paradoxical decompositions   We attach to each finite bipartite separated graph (E,C) a partial dynamical
system (\Omega(E,C), F, \theta), where \Omega(E,C) is a zero-dimensional
metrizable compact space, F is a finitely generated free group, and {\theta} is
a continuous partial action of F on \Omega(E,C). The full crossed product
C*-algebra O(E,C) = C(\Omega(E,C)) \rtimes_{\theta} F is shown to be a
canonical quotient of the graph C*-algebra C^*(E,C) of the separated graph
(E,C). Similarly, we prove that, for any *-field K, the algebraic crossed
product L^{ab}_K(E,C) = C_K(\Omega(E,C)) \rtimes_\theta^{alg} F is a canonical
quotient of the Leavitt path algebra L_K(E,C) of (E,C). The monoid
V(L^{ab}_K(E,C)) of isomorphism classes of finitely generated projective
modules over L^{ab}_K(E,C) is explicitly computed in terms of monoids
associated to a canonical sequence of separated graphs. Using this, we are able
to construct an action of a finitely generated free group F on a
zero-dimensional metrizable compact space Z such that the type semigroup S(Z,
F, K) is not almost unperforated, where K denotes the algebra of clopen subsets
of Z. Finally we obtain a characterization of the separated graphs (E,C) such
that the canonical partial action of F on \Omega(E,C) is topologically free.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg