Hypergraph C*-algebras
Mirjam Trieb, Moritz Weber, Dean Zenner

TL;DR
This paper introduces hypergraph C*-algebras, generalizing graph and ultragraph C*-algebras, exploring their nuclearity properties, and establishing a Gauge-Invariant Uniqueness Theorem for a subclass.
Contribution
It defines hypergraph C*-algebras, analyzes their nuclearity, and extends key theorems and moves from graph C*-algebra theory to this broader context.
Findings
Hypergraph C*-algebras are not always nuclear.
A Gauge-Invariant Uniqueness Theorem is proved for a subclass.
Moves on hypergraphs generalize those in graph C*-algebra theory.
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.
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Taxonomy
TopicsAdvanced Algebra and Logic
