KK-theory of the full free product of unital C*-algebras

Emmanuel Germain (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We establish in this paper the existence of a long exact sequence in KKtheory for the füll free product of unital C*-algebras K-equivalent to nuclear ones. We will first prove the existence of e KK(S, D) such thaty^ (a) = ls in KK(S, S) and 7 * (a) = 1D in KK(D,D) for A1 and A2 K-nuclear and deduce the long exact sequences for these algebras. It was first conjectured by Cuntz in 1982 and only proved so far for C*-algebras having a one dimensional representation or for reduced (discrete) group C*-algebras. We make here a critical use of the reduced free product representation äs defined by Voiculescu äs well äs Skandalis' K-nuclearity notion.

Domains: Mathematics [math]; Operator Algebras [math.OA]

Emmanuel Germain. KK-theory of the full free product of unital C*-algebras. Journal für die reine und angewandte Mathematik, 1997, 1997 (485), pp.1 - 10. ⟨10.1515/crll.1997.485.1⟩. ⟨hal-01876561⟩