Nuclearity of hypergraph $C$*-algebras

Abstract

We partially characterize nuclearity for the recently introduced class of hypergraph $C^{\ast }$-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 Sørensen to classify unital graph $C^{\ast }$-algebras. In particular, we obtain a new proof of the fact that every graph $C^{\ast }$-algebra associated to a finite graph is nuclear.