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.
|Number of pages||17|
|Journal||Journal of Pure and Applied Algebra|
|Publication status||Published - 24 May 2001|