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.
@article{bwmeta1.element.doi-10_1515_spma-2015-0012,
author = {Ilwoo Cho and Palle E. T. Jorgensen},
title = {Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs},
journal = {Special Matrices},
volume = {3},
year = {2015},
zbl = {1319.05150},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0012}
}
Ilwoo Cho; Palle E. T. Jorgensen. Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0012/
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