Classification of sectors of the Cuntz algebras by graph invariants

Katsunori Kawamura

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Classification of sectors of the Cuntz algebras by graph invariants

Katsunori Kawamura

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Abstract

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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Katsunori Kawamura. 2005-07-19. Classification of sectors of the Cuntz algebras by graph invariants. https://arxiv.org/abs/math/0507376

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