@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}
}