Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2017, 5(2), 31-56
DOI: 10.12691/tjant-5-2-2
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p-Adic Number Fields Acting On W*-Probability Spaces

Ilwoo Cho1,

1Department of Mathematics, 421 Ambrose Hall, Saint Ambrose University, 518 W. Locust St., Davenport, Iowa, 52803, U. S. A.

Pub. Date: February 15, 2017

Cite this paper:
Ilwoo Cho. p-Adic Number Fields Acting On W*-Probability Spaces. Turkish Journal of Analysis and Number Theory. 2017; 5(2):31-56. doi: 10.12691/tjant-5-2-2


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.

Free Probability Free Probability Spaces p-Adic Number Fields Von Neumann Algebras W*-Dynamical Systems Crossed Product W*-Algebras.

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