Generalised morphisms of -graphs: -morphs

Authors:
Alex Kumjian, David Pask and Aidan Sims

Journal:
Trans. Amer. Math. Soc. **363** (2011), 2599-2626

MSC (2000):
Primary 46L05

DOI:
https://doi.org/10.1090/S0002-9947-2010-05152-9

Published electronically:
December 20, 2010

MathSciNet review:
2763728

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In a number of recent papers, -graphs have been constructed from -graphs by inserting new edges in the last dimensions. These constructions have been motivated by -algebraic considerations, so they have not been treated systematically at the level of higher-rank graphs themselves. Here we introduce -morphs, which provide a systematic unifying framework for these various constructions. We think of -morphs as the analogue, at the level of -graphs, of -correspondences between -algebras. To make this analogy explicit, we introduce a category whose objects are -graphs and whose morphisms are isomorphism classes of -morphs. We show how to extend the assignment to a functor from this category to the category whose objects are -algebras and whose morphisms are isomorphism classes of -correspondences.

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Additional Information

**Alex Kumjian**

Affiliation:
Department of Mathematics (084), University of Nevada, Reno, Nevada 89557-0084

Email:
alex@unr.edu

**David Pask**

Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia

Email:
dpask@uow.edu.au

**Aidan Sims**

Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia

Email:
asims@uow.edu.au

DOI:
https://doi.org/10.1090/S0002-9947-2010-05152-9

Keywords:
$C^{*}$-algebra,
graph algebra,
$k$-graph,
$C^{*}$-correspondence.

Received by editor(s):
December 6, 2007

Received by editor(s) in revised form:
June 30, 2009

Published electronically:
December 20, 2010

Additional Notes:
This research was supported by the Australian Research Council.

Article copyright:
© Copyright 2010
American Mathematical Society