On triangular subalgebras of groupoidC*-algebras

Let ℬ be an AFC*-algebra with Stratila-Voiculescu masaD and letU be a maximal triangular subalgebra of ℬ with diagonalD. Peters, Poon and Wagner showed thatU need not be aC*-subdiagonal subalgebra of ℬ in the sense of Kawamura and Tomiyama. We investigate and explain this phenomena here from the perspective of groupoidC*-algebras by representing257-7 as the “incidence algebra” associated with a topological partial order. A number of examples are given showing what can keep a maximal triangular algebra from beingC*-subdiagonal. Supported by a grant from the National Science Foundation.