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2015 | 3 | 1 |

Tytuł artykułu

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

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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.


  • St. Ambrose Univ., Dept. of Math. & Stat., 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803,
    U. S. A. / Univ. of Iowa, Dept. of Math., 14 McLean Hall, Iowa City, Iowa, 52242, U. S. A.
  • St. Ambrose Univ., Dept. of Math. & Stat., 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803,
    U. S. A. / Univ. of Iowa, Dept. of Math., 14 McLean Hall, Iowa City, Iowa, 52242, U. S. A.


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