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

David Pask, Iain Raeburn, Trent Yeend

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

A free action α of a group G on a row-finite directed graph E induces an action α* on its Cuntz-Krieger C*-algebra C*(E), and a recent theorem of Kumjian and Pask says that the crossed product C*(E)×α*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.

Original languageEnglish
Pages (from-to)297-313
Number of pages17
JournalJournal of Pure and Applied Algebra
Volume159
Issue number2-3
DOIs
Publication statusPublished - 24 May 2001
Externally publishedYes

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