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A remark on the Kasparov groups Exti(A, B)

par Valette, Alain
Référence Pacific journal of mathematics, 109, 1, page (247-255)
Publication Publié, 1983

Article révisé par les pairs

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Résumé :

Let A and B be C*-algebras. We show that, under reasonable assumptions (A unital, nuclear and separable, B with a strictly positive element), the groups Exti(A, B) of Kasparov are isomorphic-up to a shift of dimension to the AT-theory groups of some commutant of A in the outer multiplier algebra of B o× K. The main tool to prove this is Kasparov’s "generalized theorem of Voiculescu". Following an idea of Paschke, we use our result to get a part of the "generalized Pimsner-Voiculescu exact sequence" for crossed products. © 1983 by Pacific Journal of Mathematics.