• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.1-23
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• 2019

Let ${\mathcal{G}}$ be an ultragraph and let $C^*({\mathcal{G}})$ be the associated $C^*$-algebra introduced by 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-Rørdam) via Fell bundles.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.21-43
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• 2020

We introduce the Leavitt path algebras of ultragraphs and we characterize their ideal structures. We then use this notion to introduce and study the algebraic analogy of Exel-Laca algebras.