Hypergraph C*-algebras

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.