C*-Algebras Associated with Iterated Function Systems

Abstract

We review Kajiwara and Watatani's construction of a C*-algebra from an iterated function system (IFS). If the IFS satisfies the finite branch condition or the open set condition, we build an injective homomorphism from Kajiwara-Watatani algebras to the Cuntz algebra, which can be thought as the algebra of the lifted system, and we give the description of its image. Finally, if the IFS admits a left inverse we show that the Kajiwara-Watatani algebra is isomorphic to an Exel's crossed product.

11 pages

References in corpus (3)

• A construction of $C^{\ast }$-algebras from $C^{\ast }$-correspondences
• C^*-algebras associated with self-similar sets
• KMS states on C^*-algebras associated with self-similar sets

Cited by in corpus (3)

• Traces on cores of C*-algebras associated with self-similar maps
• Ideals of the core of C*-algebras associated with self-similar maps
• Dimension groups for self-similar maps and matrix representations of the core of the associated C*-algebras