Hypergraph C*-algebras

2024/05/15 by Mirjam Trieb, Trieb, Mirjam, Moritz Weber +3 · 2 citations
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2405.09214

openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a definition of hypergraph C*-algebras. These generalize the well-known graph C*-algebras as well as ultragraph C*-algebras. In contrast to those objects, hypergraph C*-algebras are not always nuclear. We provide a number of non-nuclear examples, we prove a Gauge-Invariant Uniqueness Theorem for a subclass of hypergraph C*-algebras and we study moves on hypergraphs which generalize the moves in the theory of graph C*-algebras.

Cited by

• Hypercube C*-algebras and an application to magic isometries
• Classification of Certain C*-Algebras Generated by Two Partitions of Unity

Related

• Nuclearity of Hypergraph C*-Algebras
• A unified approach to Exel-Laca algebras and C*-algebras associated to graphs
• Simplicity of ultragraph algebras
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras I, fundamental results
• C*-algebras of labelled graphs