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Apr 25, 2011 at 21:37 comment added Theo Johnson-Freyd This is a good question, but probably not a great fit for this forum --- it easily arises (and is worded as if it has arisen) as a homework problem in a first course on Lie theory. Since it has been answered and accepted, it's not a big deal.
Apr 25, 2011 at 12:28 vote accept Son Lam Ho
Apr 25, 2011 at 12:28 comment added Son Lam Ho I'm sorry but it's not quite clear to me how the problem follows from the identification $T(G\times G)=TG\times TG$.
Apr 25, 2011 at 11:50 answer added S. Carnahan timeline score: 11
Apr 25, 2011 at 11:47 comment added agt About some of following answers: Excuse me, but is not the content of the question exactly to prove that $T_{e,e}\mu(\xi,\eta)=\xi+\eta$ for any $\xi,\eta\in T_eG$? So we should not appeal to it in a proof. But we should point out that this expression is just a consequence of the canonical identification of $T(G\times G)$ with the direct product $TG\times TG$.
Apr 25, 2011 at 11:15 answer added Eric O. Korman timeline score: 6
Apr 25, 2011 at 10:58 answer added Johannes Ebert timeline score: 0
Apr 25, 2011 at 10:32 answer added Mark timeline score: 2
Apr 25, 2011 at 10:15 vote accept Son Lam Ho
Apr 25, 2011 at 10:16
Apr 25, 2011 at 9:26 answer added darij grinberg timeline score: 1
Apr 25, 2011 at 8:47 history asked Son Lam Ho CC BY-SA 3.0