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
• DOI: 10.1016/s0022-4049(00)00191-2

✦ 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.