ISSN:
1573-0514
Keywords:
Kasparov theory
;
universal property
;
proper group action
;
equivariant stabilization theorem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let G be a locally compact group. We describe elements of KK G (A, B) by equivariant homomorphisms, following Cuntz's treatment in the non-equivariant case. This yields another proof for the universal property of KK G : It is the universal split exact stable homotopy functor. To describe a Kasparov triple (ε, ϕ, F) for A, B by an equivariant homomorphism, we have to arrange for the Fredholm operator F to be equivariant. This can be done if A is of the form $${\mathbb{K}}(L^2 G) \otimes A\prime $$ ; and more generally if the group action on A is proper in the sense of Exel and Rieffel.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1026536332122
