%0 Journal Article
%T Classification of sectors of the Cuntz algebras by graph invariants
%A Katsunori Kawamura
%J Mathematics
%D 2005
%I arXiv
%X A unitary equivalence class of endomorphisms of a unital C$^{*}$-algebra ${\cal A}$ is called a {\it sector} of ${\cal A}$. We introduced permutative endomorphisms of the Cuntz algebra ${\cal O}_N$ in the previous work. Branching laws of permutative representations of ${\cal O}_N$ by them are computed by directed regular graphs. In this article, we classify sectors associated with permutative endomorphisms of ${\cal O}_N$ by their graph invariants concretely.
%U http://arxiv.org/abs/math/0507376v1