AF-embedding of the crossed products of AH-algebras by finitely generated abelian groups
نویسنده
چکیده
LetX be a compact metric space and let Λ be a Z (k ≥ 1) action onX.We give a solution to a version of Voiculescu’s problem of AF-embedding: The crossed product C(X) ⋊Λ Z k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive Λ-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let Λ : G → Aut(C) be a monomorphism. We show that C ⋊Λ G can be embedded into a unital simple AF-algebra if and only if C admits a faithful Λ-invariant tracial state.
منابع مشابه
AF-embedding of the crossed products of AH-algebras by a finitely generated abelian groups
LetX be a compact metric space and let Λ be a Z (k ≥ 1) action onX.We give a solution to a version of Voiculescu’s problem of AF-embedding: The crossed product C(X) ⋊Λ Z k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive Λ-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let Λ : G → Aut(...
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