Isomoprhism of generalized Bratteli diagrams

Abstract

We study the notion of isomorphism for generalized Bratteli diagrams and investigate properties preserved under isomorphism. We show that every generalized Bratteli diagram is isomorphic to an irreducible generalized Bratteli diagram. We introduce the notion of a completely irreducible generalized Bratteli diagram, namely, a diagram that is isomorphic only to irreducible generalized Bratteli diagrams. We establish connections between this notion and the topological properties of the path space of a generalized Bratteli diagram and its tail equivalence relation. We examine in detail several classes of generalized Bratteli diagrams that illustrate these results.