Nuclearity of Hypergraph C*-Algebras

TL;DR

This paper investigates the nuclearity property of hypergraph C*-algebras, providing a partial characterization using a new hypergraph minor relation and offering a novel proof for nuclearity of finite graph C*-algebras.

Contribution

It introduces a hypergraph minor relation to characterize nuclearity in hypergraph C*-algebras and offers a new proof for the nuclearity of finite graph C*-algebras.

Findings

Hypergraph minor relation helps characterize nuclearity.

Finite graph C*-algebras are nuclear.

New proof technique for nuclearity.

Abstract

We partially characterize nuclearity for the recently introduced class of hypergraph C*-algebras using a tailor-made hypergraph minor relation. The latter is generated by certain operations on hypergraphs which resemble the moves on directed graphs used by Eilers, Restorff, Ruiz and S{\o}rensen to classify unital graph C*-algebras. In particular, we obtain a new proof of the fact that every graph C*-algebra associated to a finite graph is nuclear.