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Mathematics 2015, 3(4), 1095-1138; doi:10.3390/math3041095

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

1
Department of Mathematics, St. Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
2
Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA 52242, USA
*
Authors to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
Received: 26 May 2015 / Revised: 18 September 2015 / Accepted: 23 September 2015 / Published: 2 December 2015
(This article belongs to the Special Issue Mathematical physics)
View Full-Text   |   Download PDF [363 KB, uploaded 2 December 2015]

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 ℚp (for primes p), and free probability on the subalgebra Φ, generated by the Euler totient function ϕ, 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 ℚp under free-probabilistic (and hence, spectral-theoretic) techniques. View Full-Text
Keywords: p-Adic number fields ℚp; p-Adic von neumann algebras ℳp; dynamical systems induced by ℚp; arithmetic functions; the arithmetic algebra A; the euler totient function ϕ p-Adic number fields ℚp; p-Adic von neumann algebras ℳp; dynamical systems induced by ℚp; arithmetic functions; the arithmetic algebra A; the euler totient function ϕ
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Cho, I.; Jorgensen, P.E.T. Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function. Mathematics 2015, 3, 1095-1138.

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