The primitive ideal space of twisted covariant systems with continuously varying stabilizers.
Maximality of dual coactions on sectional C*-algebras of Fell bundles and applications
We give a simple proof of the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles over locally compact groups. This result was only known for discrete groups or for saturated (separable) Fell bundles over locally compact groups. Our proof, which is derived as an application of the theory of universal generalised fixed-point algebras for weakly proper actions, is different from these previously known cases and works for general Fell bundles over locally compact groups....
Crossed products whose primitive ideal spaces are generalized trivial ...-bundles.
The Connes-Kasparov conjecture for almost connected groups and for linear -adic groups
Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C-algebra of G is an isomorphism. The same is shown for the groups of -rational points of any linear algebraic group over a local field of characteristic zero.
On the K-theory of the -algebra generated by the left regular representation of an Ore semigroup
We compute the -theory of -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the -theory of these semigroup -algebras in terms of the -theory for the reduced group -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.
Permanence properties of the Baum-Connes conjecture.
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