Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kishimoto's Conjugacy Theorems in simple $C^*$-algebras of tracial rank
  one   Let $A$ be a unital separable simple amenable $C^*$-algebra with finite
tracial rank which satisfies the Universal Coefficient Theorem (UCT). Suppose
$\af$ and $\bt$ are two automorphisms with the Rokhlin property that {induce
the same action on the $K$-theoretical data of $A$.} We show that $\af$ and
$\bt$ are strongly cocycle conjugate and uniformly approximately conjugate,
that is, there exists a sequence of unitaries $\{u_n\}\subset A$ and a sequence
of strongly asymptotically inner automorphisms $\sigma_n$ such that $$ \af={\rm
Ad}\, u_n\circ \sigma_n\circ \bt\circ \sigma_n^{-1}\andeqn
\lim_{n\to\infty}\|u_n-1\|=0, $$ and that the converse holds. {We then give a
$K$-theoretic description as to exactly when $\af$ and $\bt$ are cocycle
conjugate, at least under a mild restriction. Moreover, we show that given any
$K$-theoretical data, there exists an automorphism $\af$ with the Rokhlin
property which has the same $K$-theoretical data.

10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin