On Dynamical Systems Induced by the Adele Ring

Ilwoo Cho
Ilwoo Cho
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Abstract

In this paper, we construct a dynamical system induced by the Adele ring ; based on the dynamical systems induced by -adic number fields ; for all primes : We study fundamental operator-theoretic and operator-algebraic properties of the corresponding crossed product operator algebra generated by such a dynamical system, via free probability.

References

18 Cites in Article
  1. William Arveson (2002). Generators of non-commutative dynamics.
  2. William Arveson (2003). Interaction Theory.
  3. D Bump (1996). Automorphic Forms and Representations.
  4. I Cho (2013). Operators Induced by Prime Numbers.
  5. Ilwoo Cho (2014). p-adic Banach space operators and adelic Banach space operators.
  6. I Cho (2014). Dynamical Systems on Arithmetic Functions Determined by Primes.
  7. I Cho (2014). Free Distributional Data of Arithmetic Functions and Corresponding Generating Functions.
  8. Ilwoo Cho (2011). Histories Distorted by Partial Isometries.
  9. I Cho (2010). Frames, Fractals and Radial Operators in Hilbert Space.
  10. Ilwoo Cho (2015). On dynamical systems induced by p-adic number fields.
  11. I Cho,P Jorgensen (2013). Krein-Space Operators Induced by Dirichlet Characters.
  12. I Cho,P Jorgensen (2014). Krein-Space Representations of Arithmetic Functions Determined by Primes.
  13. T Gillespie (2010). Superposition of Zeroes of Automorphic L-Functions and Functoriality.
  14. T Gillespie (2011). Prime Number Theorems for Rankin-Selberg L-Functions over Number Fields.
  15. F Radulescu (1994). Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index.
  16. R Speicher (1998). Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory.
  17. Dan Voiculescu,Kenneth Dykema,Alexandru Nica (1992). Free Random Variables.
  18. V Vladimirov,I Volovich,E Zelenov (1994). p-Adic Analysis and Mathematical Physics.
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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Ilwoo Cho. 2015. \u201cOn Dynamical Systems Induced by the Adele Ring\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 15 (GJSFR Volume 15 Issue F4).

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  • Open Access
  • CC-BY-ND-NC 4.0
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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Not Found
Classification
GJSFR-F Classification MSC 2010: 05E15
11G15
11R04
11R09
11R47
11R56
46L10
46L40
46L53
46
  • Submission ReceivedMarch 20, 2015
  • Peer Review Double Blind
    Handling Editor
  • Accepted April 13, 2015
  • Published April 26, 2015
Version of record

v1.2

Issue date
June 4, 2015

Language
en
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On Dynamical Systems Induced by the Adele Ring

Ilwoo Cho
Ilwoo Cho
  • Submission ReceivedMarch 20, 2015
  • Peer Review Double Blind
    Handling Editor
  • Accepted April 13, 2015
  • Published April 26, 2015

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