  This note presents an analysis of a class of operator algebras constructed as
cross-sectional algebras of flat holomorphic matrix bundles over a finitely
bordered Riemann surface. These algebras are partly inspired by the bundle
shifts of Abrahamse and Douglas. The first objective is to understand the
boundary representations of the containing $C^*$-algebra, i.e. Arveson's
noncommutative Choquet boundary for each of our operator algebras. The boundary
representations of our operator algebras for their containing $C^*$-algebras
are calculated, and it is shown that they correspond to evaluations on the
boundary of the Riemann surface. Secondly, we show that our algebras are
Azumaya algebras, the algebraic analogues of $n$-homogeneous $C^*$-algebras.
