BAUMSLAG–SOLITAR GROUP C∗-ALGEBRAS FROM INTERVAL MAPS

• Autor(a) principal: Correia Ramos, Carlos
• Data de Publicação: 2014
• Outros Autores: El Harti, R, Martins, Nuno, Pinto, Paulo. R.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Texto Completo: http://hdl.handle.net/10174/13078; https://doi.org/10.15352/bjma/1381782093
• topic: Group C∗-algebras, representations of C∗-algebras; symbolic dynamics, interval maps.

We yield operators U and V on Hilbert spaces that are parame- terized by the orbits of certain interval maps that exhibit chaotic behavior and obey the (deformed) Baumslag–Solitar relation UV =e2πiαVUn, α∈R, n∈N. We then prove that the scalar e2πiα can be removed whilst retaining the isomor- phism class of the C∗-algebra generated by U and V . Finally, we simultane- ously unitarize U and V by gluing pairs of orbits of the underlying noninvertible dynamical system and investigate these unitary representations under distinct pairs of orbits.