Noncommutative Functions, Matrix Bundles, and Azumaya Algebras

We study noncommutative function algebras as subalgebras of n-homogeneous C*-algebras. These algebras may be viewed as cross sections of certain holomorphic matrix bundles which arise naturally in noncommutative function theory and geometric invariant theory. We describe the connection between these algebras and bundles, and show that the function algebras we consider are Azumaya algebras.