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arXiv · 1704.05053

Primitive ideals and pure infiniteness of ultragraph $C^*$-algebras

Hossein Larki
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Abstract

Let $\mathcal{G}$ be an ultragraph and let $C^*(\mathcal{G})$ be the associated $C^*$-algebra introduced by Mark Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*(\mathcal{G})$, we approach the quotient $C^*$-algebra $C^*(\mathcal{G})/I_{(H,B)}$ by the $C^*$-algebra of finite graphs and prove versions of gauge invariant and Cuntz-Krieger uniqueness theorems for it. We then describe primitive gauge invariant ideals and determine purely infinite ultragraph $C^*$-algebras (in the sense of Kirchberg-R${\o}$rdam) via Fell bundles.

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Hossein Larki. 2017-04-16. Primitive ideals and pure infiniteness of ultragraph $C^*$-algebras. https://arxiv.org/abs/1704.05053

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