On C∗-Algebras from Interval Maps
Given a unimodal interval map f , we construct partial isometries acting on Hilbert spaces associated to the orbit of each point. Then we prove that such partial isometries give rise to representations of a C∗-algebra associated to the subshift encoding the kneading sequence of the critical point. T...
| Main Author: | |
|---|---|
| Format: | article |
| Language: | eng |
| Published: |
2014
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10174/10099 |
| Country: | Portugal |
| Oai: | oai:dspace.uevora.pt:10174/10099 |
| Summary: | Given a unimodal interval map f , we construct partial isometries acting on Hilbert spaces associated to the orbit of each point. Then we prove that such partial isometries give rise to representations of a C∗-algebra associated to the subshift encoding the kneading sequence of the critical point. This construction has the advantage of incorporating maps with a non necessarily Markov partition (e.g. Fibonacci unimodal map). If we are indeed in the presence of a finite Markov partition, then we prove that these new representations coincide with the (previously considered by the authors) representations arising from the Cuntz–Krieger algebra of the underlying (finite) transition matrix. |
|---|