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

Ilwoo Cho; Palle Jorgensen

doi:10.3390/math3041095

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

Journal article

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

Ilwoo Cho and Palle Jorgensen

Mathematics, Vol.3(4), pp.1095-1138

12/01/2015

DOI: 10.3390/math3041095

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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.

Adic number fields ℚp

Adic von neumann algebras ℳp

arithmetic functions

dynamical systems induced by ℚp

Mathematics

the arithmetic algebra A

the euler totient function ϕ

Details

Title: Subtitle: Free W-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function
Creators: Ilwoo Cho
Palle Jorgensen
Resource Type: Journal article
Publication Details: Mathematics, Vol.3(4), pp.1095-1138
DOI: 10.3390/math3041095
ISSN: 2227-7390
eISSN: 2227-7390
Publisher: MDPI AG
Language: English
Date published: 12/01/2015
Academic Unit: Mathematics
Record Identifier: 9984241054302771

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