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Visualizing Automorphisms of Graph Algebras

Part of: Selfadjoint operator algebras Topological dynamics

Published online by Cambridge University Press:  01 February 2018

James Emil Avery ,
Rune Johansen  and
Wojciech Szymański
James Emil Avery*
Affiliation:
Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 København Ø, Denmark (avery@nbi.ku.dk)
Rune Johansen
Affiliation:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 København Ø, Denmark (rune@cyx.dk)
Wojciech Szymański
Affiliation:
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark (szymanski@imada.sdu.dk)
*
*Corresponding author.
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Abstract

Many fundamental properties of graph C*-algebras may be determined directly from the structure of the underlying graph, and because of this, they have been celebrated as C*-algebras that can be seen. This paper shows how permutative endomorphisms of graph C*-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.

Keywords

graph algebrapermutative endomorphismautomorphismtextile system

MSC classification

Primary: 46L40: Automorphisms
Secondary: 37B10: Symbolic dynamics
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 1 , February 2018 , pp. 215 - 249
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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