Free W * -Dynamical Systems From p -Adic Number Fields and the Euler Totient Function

Ilwoo Cho and Palle E. T. Jorgensen
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Ilwoo Cho: Department of Mathematics, St. Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
Palle E. T. Jorgensen: Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA 52242, USA

Mathematics, 2015, vol. 3, issue 4, 1-44

Abstract: In this paper, we study relations between free probability on crossed product W * -algebras with a von Neumann algebra over p-adic number fields ? p (for primes p), and free probability on the subalgebra ?, generated by the Euler totient function ?, of the arithmetic algebra A , consisting of all arithmetic functions. In particular, we apply such free probability to consider operator-theoretic and operator-algebraic properties of W * -dynamical systems induced by ?p under free-probabilistic (and hence, spectral-theoretic) techniques.

Keywords: p -Adic number fields ? p; p -Adic von neumann algebras ? p; dynamical systems induced by ?p; arithmetic functions; the arithmetic algebra A; the euler totient function ? (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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