In fact "most" simple groups have such covers: if and only if there is a long real root. There is a long and rich history of this topic, going back at least to a paper by Jacque Tits from 1967 (as well as some older work which appeared only in Russian). For a uniform (case-free) treatment see Nonlinear covers of real groups, MR2112326. Also see the references in the paper and in the Mathscinet review.
Jeffrey Adams
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