Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finiteness and Paradoxical Decompostions in C*-Dynamical Systems   We discuss the interplay between K-theoretical dynamics and the structure
theory for certain C*-algebras arising from crossed products. For
noncommutative C*-systems we present notions of minimality and topological
transitivity in the K-theoretic framework which are used to prove structural
results for reduced crossed products. In the presence of sufficiently many
projections we associate to each noncommutative C*-system (A,G) a type
semigroup S(A,G) which reflects much of the spirit of the underlying action. We
characterize purely infinite as well as stably finite crossed products by means
of the infinite or rather finite nature of this semigroup. We explore the
dichotomy between stable finiteness and pure infiniteness in certain classes of
reduced crossed products by means of paradoxical decompositions.

1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom