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International Mathematics Research Papers (2008) Vol. 2008 : article ID rpn007, 67 pages, doi:10.1093/imrp/rpn007 published on August 27, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

AF-Embeddings of the Crossed Products of AH-Algebras by Finitely Generated Abelian Groups

Huaxin Lin1

Department of Mathematics, East China Normal University, Shanghai, China

Correspondence: Correspondence to be sent to: hlin{at}uoregon.edu

Let X be a compact metric space and let {Lambda} be a Zk (k ≥ 1) action on X. We give a solution to a version of Voiculescu's problem of AF-embedding: The crossed product C(X) {rtimes}{Lambda} Zk can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive {Lambda}-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let {Lambda} : G -> Aut(C) be a monomorphism. We show that C {rtimes}{Lambda} G can be embedded into a unital simple AF-algebra if and only if C admits a faithful {Lambda}-invariant tracial state.

1 Present Address: Department of Mathematics, University of Oregon, Eugene, Oregon 97403, USA



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