2025/09/01 by Schäfer, Björn · 1 citation
#46L35 (Primary) 46L09 #47C15 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2509.01309
We study C*-algebras generated by two partitions of unity subject to orthogonality relations governed by a bipartite graph which we also call "bipartite graph C*-algebras". These algebras generalize at the same time the C*-algebra C^∗(p,q) generated by two projections and the hypergraph C*-algebras of Trieb, Weber and Zenner. We describe alternative universal generators of bipartite graph C*-algebras and study partitions of unity in generic position associated to a bipartite graph. As a main result, we prove that bipartite graph C*-algebras are completely classified by their one- and two-dimensional irreducible representations which provides a first step towards a classification of the more general hypergraph C*-algebras.