The Connes-Kasparov conjecture for almost connected groups and for linear p-adic groups

By J. Chabert, S. Echterhoff, R. Nest. 2001

116 citations recorded by the source corpus.

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 k-rational points of any linear algebraic group over a local field k of characteristic zero.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/85679c58e7c665991476b89edb3bd1e3e39f0900

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In Algebra and Number Theory

1. W. Lück
2. H. Reich
3. S. Echterhoff
4. J. Chabert
5. J. Tu
6. H. Oyono-Oyono
7. Vincent Lafforgue
8. Arthur Bartels

In Mathematical Physics

1. W. Lück
2. H. Reich
3. S. Echterhoff
4. J. Chabert
5. Vincent Lafforgue
6. J. Tu
7. Arthur Bartels
8. H. Oyono-Oyono

Citations in the corpus

• The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ) (2006, unknown): “Indeed, let Ω: G×G→ C ( [0, 1], T ) be a 2-cocycle with evaluations ωx = Ω( · , · )(x) for x ∈ [0, 1].”
• Banach KK-theory and the Baum-Connes conjecture (2003, background): “As a consequence of this result the Baum-Connes conjecture has been proven for all almost connected groups by Chabert, Echterhoff and Nest ([9]).”
• Going-down functors, the Künneth formula, and the Baum-Connes conjecture (2004, background): “We also know from [ CEN ] that (the k-rational points of) linear algebraic groups over local fields of characteristic 0 satisfy BC for C. By [GK, Theorem 5.4] and [D] all such groups have type I reduced group algebras C ∗ r (G), which therefore satisfy the K¨ unneth formula.”
• The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, methodology): “The Baum– Connes Conjecture for second countable almost connected groups G has been proven by Chabert–Echterhoff–Nest [60] based on the work of Higson–Kasparov [149] and Lafforgue [186].”
• Non-Hausdorff groupoids, proper actions and $K$-theory (2004, background): “top(G) and an assembly map µ: Ktop∗(G) →K∗(C∗ r(G)) (see also [25, 27]). When G is a group, the map µis known to be an isomorphism in many cases, such as almost connected groups, linear p-adic groups [7], a-T-menable groups [10] and hyperbolic discrete groups [22]. For groupoids, the situation is, u”