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AF-embedding of the crossed products of AH-algebras by finitely generated abelian groups

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 نشر من قبل Huaxin Lin
 تاريخ النشر 2007
  مجال البحث
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 تأليف Huaxin Lin




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Let $X$ be a compact metric space and let $Lambda$ be a $Z^k$ ($kge 1$) action on $X.$ We give a solution to a version of Voiculescus problem of AF-embedding: The crossed product $C(X)rtimes_{Lambda}Z^k$ 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 $Lambda: Gto Aut(C)$ be a monomorphism. We show that $Crtimes_{Lambda} G$ can be embedded into a unital simple AF-algebra if and only if $C$ admits a faithful $Lambda$-invariant tracial state.



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