Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groupoid approach to the dynamical system of commutative von Neumann
  Algebras   The automorphism group $Aut(X,\mu)$ of a compact, complete metric space $X$
with a Radon measure $\mu$ is a subgroup of $\mathcal{U}(L^2(X,\mu))$-the
unitary group of operators on $L^2(X,\mu)$. The $Aut(X,\mu)$-action on the
generalized space $\mathcal{M}(X)$ is a proper action. Hence, there exists a
slice at each point of the generalized space $\mathcal{M}(X)$. Measure Groupoid
(virtual group) is subsequently employed to analyze the resulting dynamical
system as that of the ergodic action of the commutative algebra (a lattice)
$C(X)$ on the generalized space $\mathcal{M}(X)$ which is represented on a
commutative von Neumann algebra.

32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio