@article{tjant2017522,
author={Cho, Ilwoo},
title={*p*-Adic Number Fields Acting On *W*^{*}-Probability Spaces},
journal={Turkish Journal of Analysis and Number Theory},
volume={5},
number={2},
pages={31--56},
year={2017},
url={http://pubs.sciepub.com/tjant/5/2/2},
issn={2333-1232},
abstract={In this paper, we study how a *p*-adic number field acts on an arbitrarily fixed *W*^{*}-algebra, and how it affects the original free-probabilistic information on the *W*^{*}-algebra, for each prime *p*. In particular, by understanding the σ-algebra of as a semigroup equipped with the setintersection, we act on a unital tracial *W*^{*}-probability space (*M*,*tr*), creating the corresponding semigroup *W*^{*}-dynamical system. From such a dynamical system, construct the crossed product *W*^{*}-algebra equipped with a suitable linear functional. We study free probability on such *W*^{*}-dynamical operator-algebraic structures determined by primes, and those on corresponding free products of such structures over primes. As application, we study cases where given *W*^{*}-probability spaces are generated by countable discrete groups.},
doi={10.12691/tjant-5-2-2}
publisher={Science and Education Publishing}
}