C*-algebras Associated do Stationary Ordered Bratteli Diagrams

TL;DR

This paper constructs C*-algebras from substitution-based Bratteli diagrams, demonstrating their invariance under diagram equivalence and establishing their role as complete invariants for diagram classification.

Contribution

It introduces a new C*-algebra associated with substitution Bratteli diagrams and proves its invariance and completeness as an invariant for diagram equivalence.

Findings

C*-algebras contain the partial crossed product of the Bratteli-Vershik system

Algebras are invariant under Bratteli diagram equivalence

Isomorphism class with generators is a complete invariant

Abstract

In this paper, we introduce a C*-algebra associated to any substitution (via its Bratteli diagram model). We show that this C*-algebra contains the partial crossed product C*-algebra of the corresponding Bratteli-Vershik system and show that these algebras are invariant under equivalence of the Bratteli diagrams. We also show that the isomorphism class of the algebras, together with a distinguished set of generators, is a complete invariant for equivalence of Bratteli diagrams.