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I am trying to find out how the Baum-Connes conjecture works over $GL(1)$ over local fiels.

I am just wondering if anybody knows how to get a countable many generators for in the L.H.S of the Baum-Connes conjecture over $GL(1)$:

$\mu: K_{j}^{G}(\beta G)\to K_{j}(C_{r}^{*}G)$,

where the $L.H.S.$ is the $K$-homology of the tree for $GL(1)$, and the R.H.S. is the $K$-theory group of reduce $C^{*}$-algebra of same group $G$.

Thanks a lot.

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Do you mean ${\rm GL}(1)$ or ${\rm GL}(2)$ ? –  Paul Broussous Jul 6 '11 at 15:29
It Was on $GL(1,F)$ and $GL(1,E)$ where $E$ is an extension of $F$ but I have already solved it while ago But am working on $GL(2)$ now so if have you got any tips that would be great Thanks Paul –  Dragon Jul 8 '11 at 9:26
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