Quotients of Ultragraph C*-Algebras

2015/11/25 by Hossein Larki, Larki, Hossein
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1512.00346

openalex publication_date 2015/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be an ultragraph and let C^*(G) be the associated C^*-algebra introduced by Mark Tomforde. For any gauge invariant ideal I_(H,B) of C^*(G), we analyze the structure of the quotient C^*-algebra C^*(G)/I_(H,B). For simplicity's sake, we first introduce the notion of quotient ultragraph G/(H,B) and an associated C^*-algebra C^*(G/(H,B)) such that C^*(G/(H,B))≅ C^*(G)/I_(H,B). We then prove the gauge invariant and the Cuntz-Krieger uniqueness theorems for C^*(G/(H,B)) and describe primitive gauge invariant ideals of C^*(G/(H,B)).

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