This is the first time I am using Mathoverflow and I am still learning how to use it. That is why I want to begin with a curious question:
Does the group of automorphisms of a Bruhat-Tits tree have nontrivial central extensions?
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$\begingroup$ @Hadi: it seems like a perfectly good qustion, but people might be more interested if you added some motivation. (Also, why is it tagged "ergodic-theory"?) $\endgroup$– Pete L. ClarkCommented Oct 12, 2010 at 1:15
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$\begingroup$ Are you just asking about the full automorphism group of a $q+1$-regular tree (which is quite large), or are you asking for the automorphisms to preserve some algebraic structure? $\endgroup$– S. Carnahan ♦Commented Oct 12, 2010 at 3:44
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$\begingroup$ @Pete: The automorphism group of a tree and $\mathrm{SL}_2(\mathbb Q_p)$ have similar properties. It is probably natural to guess that their central extensions look similar as well (though it may merely be a wild guess.) There are also a result by Kapoudjian what says that a combinatorial analog of $Diff(S^1)$ has nontrivial central extensions. @Scott: I mean the automorphism group which acts rigidly on edges, hence it is locally compact. $\endgroup$– HadiCommented Oct 14, 2010 at 3:00
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