Asymptotic Homomorphisms and EquivariantKK-Theory
نویسندگان
چکیده
منابع مشابه
A Note on Asymptotic Homomorphisms
Using the notion of asymptotic homomorphism due to Connes and Higson we construct bivariant homology-cohomology theories for separable C*-algebras, which satisfy general excision axioms and are nonperiodic.
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to be quasidiagonal when B⊗K contains an approximate unit of projections which is quasi-central in E, cf. [Sa]. He identified, under certain conditions, the subgroup of KK(A,B) which the quasidiagonal extensions correspond to under Kasparov’s isomorphism Ext(A,B) ' KK(A,B). C. Schochet has removed some of Salinas’ conditions in [S], the result being that when A is a unital C-algebra in the boot...
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Let A be a separable C∗-algebra and let B be a stable C∗-algebra with a strictly positive element. We consider the (semi)group Ext(A,B) (resp. Ext(A,B)) of homotopy classes of asymptotic (resp. of genuine) homomorphisms from A to the corona algebra M(B)/B and the natural map i : Ext(A,B) −→ Ext(A,B). We show that if A is a suspension then Ext(A,B) coincides with E-theory of Connes and Higson an...
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The algebra Ψ(M) of order zero pseudodifferential operators on a compact manifold M defines a well-known C∗-extension of the algebra C(S∗M) of continuous functions on the cospherical bundle S∗M ⊂ T ∗M by the algebra K of compact operators. In his proof of the index theorem, Higson defined and used an asymptotic homomorphism T from C0(T ∗M) to K, which plays the role of a deformation for the com...
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Let G be a locally compact group. We describe elements of KK(A,B) by equivariant homomorphisms, following Cuntz’s treatment in the non-equivariant case. This yields another proof for the universal property of KK: It is the universal split exact stable homotopy functor. To describe a Kasparov triple (E, φ, F ) for A,B by an equivariant homomorphism, we have to arrange for the Fredholm operator F...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1999
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3377