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Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
Journal article   Open access   Peer reviewed

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

Ilwoo Cho and Palle E. T Jorgensen
Special matrices, Vol.3(1), pp.123-154
07/08/2015
DOI: 10.1515/spma-2015-0012
url
https://doi.org/10.1515/spma-2015-0012View
Published (Version of record) Open Access

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 A = 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 A
05E15 11G15 11R04 11R09 11R47 11R56 46L10 46L40 46L53 46L54 Directed Graphs Graph Groupoids Groupoid Dynamical Systems

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