A more symmetric picture for Kasparov's KK-bifunctor

الأصل · EN

For C*-algebras A and B, we generalize the notion of a quasihomomorphism from A to B, due to Cuntz, by considering quasihomomorphisms from some C*-algebra C to B such that C surjects onto A, and the two maps forming a quasihomomorphism agree on the kernel of this surjection. Under an additional assumption, the group of homotopy classes of such generalized quasihomomorphisms coincides with KK(A,B). This makes the definition of Kasparov's bifunctor slightly more symmetric and gives more flexibility for constructing elements of KK-groups. These generalized quasihomomorphisms can be viewed as pairs of maps directly from A (instead of various C's), but these maps need not be *-homomorphisms.