Abstract
We yield C*-algebras representations on the orbit spaces from the family of interval maps f(x) = βx+α (mod 1) lifted to circle maps, in which case β ∈ N.
Each orbit will encode an unitary equivalence class of an irreducible representation of: a Cuntz algebra O β if Jα = 0 and β > 1; an irrational rotation algebra A β if α ∉ ℚ and β = 1; and a Cuntz-Krieger O Aα,β whenever β > 1 and the critical point is periodic, where A α,β is the underlying Markov transition matrix of f.
To the memory of José de Sousa Ramos
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Ramos, C.C., Martins, N., Pinto, P.R. (2008). Orbit Representations and Circle Maps. In: Bastos, M.A., Lebre, A.B., Speck, FO., Gohberg, I. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 181. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8684-9_21
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DOI: https://doi.org/10.1007/978-3-7643-8684-9_21
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