Cartan subalgebras of C*-algebras associated with complex dynamical systems
Abstract
Let $R$ be a rational function with degree $\geq 2$ and $X$ be its Julia set, its Fatou set, or the Riemann sphere. Suppose that $X$ is not empty. We can regard $R$ as a continuous map from $X$ onto itself. Kajiwara and Watatani showed that in the case that $X$ is the Julia set, $C_0(X)$ is a maximal abelian subalgebra of $\mathcal{O}_R(X)$, where $\mathcal{O}_R(X)$ denotes the C*-algebra associated with the dynamical system $(X,R)$ introduced by them. In this paper, we develop their result and give the equivalent condition for $C_0(X)$ to be a Cartan subalgebra of $\mathcal{O}_R(X)$.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Operator Algebra Research
advanced mathematical theories
Publication details
- Journal / source
- Journal of Operator Theory
- Publisher
- Theta Foundation
- Volume
- 95
- Issue
- 2
- Pages
- 339–369
- Publication date
- 30 April 2026
- Language
- EN