C*-algebras Associated do Stationary Ordered Bratteli Diagrams

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.

20 pages

References in corpus (1)

• Partial dynamical systems and C*-algebras generated by partial isometries

Cited by in corpus (3)

• The dynamics of partial inverse semigroup actions
• Leavitt path algebras as partial skew group rings
• Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics