Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
Ilwoo Cho, Palle E. T. Jorgensen (2015)
Special Matrices
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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,...