Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs

Ilwoo Cho; Palle E. T. Jorgensen

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 123-154, electronic only
  • ISSN: 2300-7451

Abstract

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In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we consider free probability on AG.

How to cite

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Ilwoo Cho, and Palle E. T. Jorgensen. "Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs." Special Matrices 3.1 (2015): 123-154, electronic only. <http://eudml.org/doc/270904>.

@article{IlwooCho2015,
abstract = {In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we consider free probability on AG.},
author = {Ilwoo Cho, Palle E. T. Jorgensen},
journal = {Special Matrices},
keywords = {Directed Graphs; Graph Groupoids; Groupoid Dynamical Systems; directed graphs; graph groupoids; groupoid dynamical systems},
language = {eng},
number = {1},
pages = {123-154, electronic only},
title = {Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs},
url = {http://eudml.org/doc/270904},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Ilwoo Cho
AU - Palle E. T. Jorgensen
TI - Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 123
EP - 154, electronic only
AB - In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we consider free probability on AG.
LA - eng
KW - Directed Graphs; Graph Groupoids; Groupoid Dynamical Systems; directed graphs; graph groupoids; groupoid dynamical systems
UR - http://eudml.org/doc/270904
ER -

References

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  1. [1] I. Cho, Operators Induced by Prime Numbers, Methods Appl. Math. Sci. 19, no. 4, (2013) 313 - 340. Zbl1332.46064
  2. [2] I. Cho, Graph Groupoids and Partial Isometries, ISBN: 978-3-8383-1397-9, (2009) Lambert Academic Press 
  3. [3] I. Cho, Classification on Arithmetic Functions and Corresponding Free-Moment L-Functions, Bulletin Korea Math. Soc., (2015) To Appear. Zbl1329.11113
  4. [4] I. Cho, p-Adic Banach-Space Operators and Adelic Banach-Space Operators, Opuscula Math., 34, no. 1, (2014) 29 - 65. Zbl06291546
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  10. [10] I. Cho, and P. E. T. Jorgensen, Krein-Space Operators Induced by Dirichlet Characters, Contemp. Math.: Commutative and Noncommutative Harmonic Analysis and Applications, (2014) 3 - 33. Zbl1322.11065
  11. [11] I. Cho, and P. E. T. Jorgensen, Actions of Arithmetic Functions on Matrices and Corresponding Representations, Ann. Funct. Anal., (2014) To Appear. Zbl1309.46037
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