Coverings of k-graphs

Coverings of k-graphs. Pask, D., Quigg, J., & Raeburn, I. Journal of Algebra, 289(1):161–191, 2005.

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz–Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a satisfactory version of the usual topological classification in terms of subgroups of a fundamental group. We then use this classification to describe the C∗-algebras of covering k-graphs as crossed products by coactions of homogeneous spaces, generalizing recent results on the C∗-algebras of graphs.

@article{pask_coverings_2005,
	title = {Coverings of k-graphs},
	volume = {289},
	issn = {0021-8693},
	url = {http://www.sciencedirect.com/science/article/pii/S0021869305001286},
	doi = {10.1016/j.jalgebra.2005.01.051},
	abstract = {k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz–Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a satisfactory version of the usual topological classification in terms of subgroups of a fundamental group. We then use this classification to describe the C∗-algebras of covering k-graphs as crossed products by coactions of homogeneous spaces, generalizing recent results on the C∗-algebras of graphs.},
	language = {en},
	number = {1},
	urldate = {2016-07-22},
	journal = {Journal of Algebra},
	author = {Pask, David and Quigg, John and Raeburn, Iain},
	year = {2005},
	keywords = {-Graph, -algebra, Coaction, Covering, Fundamental group, Small category},
	pages = {161--191},
}

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