C*-algebras Associated do Stationary Ordered Bratteli Diagrams

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.