Isomoprhism of generalized Bratteli diagrams

TL;DR

This paper explores the concept of isomorphism in generalized Bratteli diagrams, establishing their properties, classifications, and connections to topological features of their path spaces.

Contribution

It introduces the notion of completely irreducible generalized Bratteli diagrams and links their isomorphism classes to topological properties.

Findings

Every generalized Bratteli diagram is isomorphic to an irreducible one.

Introduces the concept of completely irreducible diagrams.

Connects diagram isomorphism to topological properties of path spaces.

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.