K-Theory of the Commutator Ideal

Emmanuel Germain (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We consider for unital C∗-algebras the short exact sequence 0 → 1 → A ∗C B → A ⊗max B → 0 and give an explicit formula for the boundary map for separable C∗-algebras for which the K¨unneth formula for tensor products holds without Tor-terms. In the course of the article, we study the similar case of an ideal concerning one-relator groups.

Keywords: relator groups; commutators; cyclic cohomology; Maple

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

Emmanuel Germain. K-Theory of the Commutator Ideal. K-Theory, 2001, 23 (1), pp.41 - 52. ⟨10.1023/A:1017564222199⟩. ⟨hal-01876555⟩