Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Endomorphisms of the Cuntz Algebras   This mainly expository article is devoted to recent advances in the study of
dynamical aspects of the Cuntz algebras O_n, with n finite, via their
automorphisms and, more generally, endomorphisms. A combinatorial description
of permutative automorphisms of O_n in terms of labeled, rooted trees is
presented. This in turn gives rise to an algebraic characterization of the
restricted Weyl group of O_n. It is shown how this group is related to certain
classical dynamical systems on the Cantor set. An identification of the image
in Out(O_n) of the restricted Weyl group with the group of automorphisms of the
full two-sided n-shift is given, for prime n, providing an answer to a question
raised by Cuntz in 1980. Furthermore, we discuss proper endomorphisms of O_n
which preserve either the canonical UHF-subalgebra or the diagonal MASA, and
present methods for constructing exotic examples of such endomorphisms.

36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas