Nuclearity classification for hypergraph C*-algebras

Determine for which hypergraphs HΓ the associated hypergraph C*-algebra C*(HΓ) is nuclear, i.e., characterize the class of hypergraphs whose universal C*-algebras defined from the hypergraph relations are nuclear.

Background

Hypergraph C*-algebras, introduced by Trieb, Weber, and Zenner, arise naturally in the paper of combinatorial C*-algebras built from hypergraphs. A central structural property is nuclearity. The paper notes that identifying exactly which hypergraphs yield nuclear C*-algebras remains an open problem.

The author’s prior work shows that determining nuclearity for hypergraph C*-algebras reduces to determining nuclearity for bipartite graph C*-algebras, connecting this open question to the classification of nuclearity within a broader combinatorial framework. The present paper contributes partial progress by proving nuclearity for the subclass of bipartite graphs given by hypercubes Q_n.