Equivariant Kasparov theory and generalized homomorphisms
K-Theory and Homology
2015-10-23 v2 Operator Algebras
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 (E, phi, F) 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 K(L^2G) otimes A' and more generally if the group action on A is proper in the sense of Rieffel and Exel.
Cite
@article{arxiv.math/0001094,
title = {Equivariant Kasparov theory and generalized homomorphisms},
author = {Ralf Meyer},
journal= {arXiv preprint arXiv:math/0001094},
year = {2015}
}
Comments
22 pages, final version, will appear in K-Theory added references and a few additional explanations to the text