C*-Algebras Associated with Iterated Function Systems
Operator Algebras
2019-09-11 v1 Dynamical 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.
Keywords
Cite
@article{arxiv.0811.1482,
title = {C*-Algebras Associated with Iterated Function Systems},
author = {Gilles G. de Castro},
journal= {arXiv preprint arXiv:0811.1482},
year = {2019}
}
Comments
11 pages