Classification of sectors of the Cuntz algebras by graph invariants

Details Classification of sectors of the Cuntz algebras by graph invariants Classification of sectors of the Cuntz algebras by graph invariants

2005-07-19

arxiv.org/abs/math/0507376v1

Mathematics

Operator Algebras

Scientific paper

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.

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