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

Author

Listed:
  • 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)

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 ℚ p (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.

Suggested Citation

  • Ilwoo Cho & Palle E. T. Jorgensen, 2015. "Free W * -Dynamical Systems From p -Adic Number Fields and the Euler Totient Function," Mathematics, MDPI, vol. 3(4), pages 1-44, December.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:4:p:1095-1138:d:59806
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    References listed on IDEAS

    as
    1. Alpay, Daniel & Salomon, Guy, 2013. "Non-commutative stochastic distributions and applications to linear systems theory," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2303-2322.
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