BAUMSLAG–SOLITAR GROUP C∗-ALGEBRAS FROM INTERVAL MAPS

Abstract

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.