Opuscula Math. 35, no. 4 (2015), 445-484
http://dx.doi.org/10.7494/OpMath.2015.35.4.445

Opuscula Mathematica

# On dynamical systems induced by p-adic number fields

Ilwoo Cho

Abstract. In this paper, we construct dynamical systems induced by $$p$$-adic number fields $$\mathbb{Q}_{p}$$. We study the corresponding crossed product operator algebras induced by such dynamical systems. In particular, we are interested in structure theorems, and free distributional data of elements in the operator algebras.

Keywords: prime fields, $$p$$-adic number fields, the Adele ring, $$p$$-adic von Neumann algebras, $$p$$-adic dynamical systems.

Mathematics Subject Classification: 05E15, 11R47, 46L54, 47L15, 47L55.

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• Ilwoo Cho
• St. Ambrose University, Department of Mathematics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, USA
• Revised: 2014-10-29.
• Accepted: 2014-11-07.