C*-Algebras Associated with Iterated Function Systems

Details C*-Algebras Associated with Iterated Function Systems C*-Algebras Associated with Iterated Function Systems

2008-11-10

arxiv.org/abs/0811.1482v1

Mathematics

Operator Algebras

11 pages

Scientific paper

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.

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