Inductive limits of C(X)-modules and continuous fields of AF-algebras

AbstractLet X be a compact connected space and (Ai)i = 1∞, a sequence of finite-dimensional C∗-algebras. Each inductive limit fx103-1, with C(X)-linear connecting ∗-homomorphisms, is ∗-isomorphic as C(X)-module to the C∗-algebra defined by a certain continuous field EL of AF-algebras. We classify the C∗-algebras L for which EL has simple fibres. In the general case the classification is given in the category of the C∗-algebras which are C(X)-modules