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Actions of semigroups on directed graphs and their C∗-algebras

✍ Scribed by David Pask; Iain Raeburn; Trent Yeend


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
172 KB
Volume
159
Category
Article
ISSN
0022-4049

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✦ Synopsis


A free action of a group G on a row-ÿnite directed graph E induces an action * on its Cuntz-Krieger C * -algebra C * (E), and a recent theorem of Kumjian and Pask says that the crossed product C * (E) × * G is stably isomorphic to the C * -algebra C * (E=G) of the quotient graph. We prove an analogue for free actions of Ore semigroups. The main ingredients are a new generalisation of a theorem of Gross and Tucker, dilation theory for endomorphic actions of Ore semigroups on graphs and C * -algebras, and the Kumjian-Pask Theorem itself.


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