Matrices induced by arithmetic functions,primes and groupoid actions of directedgraphs

Special Matrices

卷:3

Cho Ilwoo¹  Jorgensen Palle E. T.¹ 

[1] St. Ambrose Univ., Dept. of Math. ;

关键词: Directed Graphs;    Graph Groupoids;    Groupoid Dynamical Systems;    05E15;    11G15;    11R04;    11R09;    11R47;    11R56;    46L10;    46L40;    46L53;    46L54;   

DOI  :  10.1515/spma-2015-0012

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown