462 research outputs found
Bivariant -Theory and the Baum-Connes conjecure
This is a survey on Kasparov's bivariant -theory in connection with the
Baum-Connes conjecture on the -theory of crossed products by
actions of a locally compact group on a C*-algebra . In particular we
shall discuss Kasparov's Dirac dual-Dirac method as well as the permanence
properties of the conjecture and the "Going-Down principle" for the left hand
side of the conjecture, which often allows to reduce -theory computations
for to computations for crossed products by compact subgroups of
. We give several applications for this principle including a discussion of
a method developed by Cuntz, Li and the author for explicit computations of the
-theory groups of crossed products for certain group actions on totally
disconnected spaces. This provides an important tool for the computation of
-theory groups of semi-group C*-algebras.Comment: Some minor correction
Full duality for coactions of discrete groups
Using the strong relation between coactions of a discrete group G on
C*-algebras and Fell bundles over G, we prove a new version of Mansfield's
imprimitivity theorem for coactions of discrete groups. Our imprimitivity
theorem works for the universally defined full crossed products and arbitrary
subgroups of G, as opposed to the usual theory which uses the spatially defined
reduced crossed products and normal subgroups of G. Moreover, our theorem
factors through the usual one by passing to appropriate quotients. As
applications we show that a Fell bundle over a discrete group is amenable in
the sense of Exel if and only if the double dual action is amenable in the
sense that the maximal and reduced crossed products coincide. We also give a
new characterization of induced coactions in terms of their dual actions.Comment: 18 page
Central twisted transformation groups and group -algebras of central group extensions
We examine the structure of central twisted transformation group \cs-algebras
C_{0}(X)\rtimes_{\id,u}G, and apply our results to the group \cs-algebras of
central group extensions. Our methods require that we study Moore's cohomology
group H^{2}\bigl(G,C(X,\T)\bigr), and, in particular, we prove an inflation
result for pointwise trivial cocyles which may be of use elsewhere.Comment: 22 pages. To appear in the Indiana U. Math.
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