Visualizing Automorphisms of Graph Algebras

Abstract

Many fundamental properties of graphC*-algebras may be determined directly from the structure of the underlying graph, and because of this, they have been celebrated asC*-algebras that can be seen. This paper shows how permutative endomorphisms of graphC*-algebras can be represented by labelled directed multigraphs that give visual representations of the endomorphisms and facilitate computations. This formalism provides a useful calculus for permutative automorphisms and allows efficient exhaustive construction of such automorphisms.