Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous and discrete flows on operator algebras   Let $(N,\R,\theta)$ be a centrally ergodic W* dynamical system. When $N$ is
not a factor, we show that, for each $t\not=0$, the crossed product induced by
the time $t$ automorphism $\theta_t$ is not a factor if and only if there exist
a rational number $r$ and an eigenvalue $s$ of the restriction of $\theta$ to
the center of $N$, such that $rst=2\pi$. In the C* setting, minimality seems to
be the notion corresponding to central ergodicity. We show that if
$(A,\R,\alpha)$ is a minimal unital C* dynamical system and $A$ is either prime
or commutative but not simple, then, for each $t\not=0$, the crossed product
induced by the time $t$ automorphism $\alpha_t$ is not simple if and only if
there exist a rational number $r$ and an eigenvalue $s$ of the restriction of
$\alpha$ to the center of $A$, such that $rst=2\pi$.

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The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
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The categories of this paper are: eess