Do any of the simply connected simple Lie groups of the split real classical Lie algebras have names other than “the universal cover of _”?
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$\begingroup$ Spin? (And of course SL and Sp.) $\endgroup$– LSpiceCommented Aug 29, 2023 at 1:49
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$\begingroup$ None of those are simply connected. $\endgroup$– Daniel SebaldCommented Aug 29, 2023 at 3:03
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2$\begingroup$ @DanielSebald The spin group ( as discussed in en.wikipedia.org/wiki/Spin_group ) is definitely simply connected for $n > 2$. $\endgroup$– Sam HopkinsCommented Aug 29, 2023 at 3:11
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2$\begingroup$ That only applies to the definite spin groups. The split spin groups have fundamental groups of order 2 for $n>5$. $\endgroup$– Daniel SebaldCommented Aug 29, 2023 at 3:29
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2$\begingroup$ In a sense, the title is slightly confusing, since "split" is an inessential restriction: the topic is really "Names for universal covers of classical Lie groups". $\endgroup$– YCorCommented Aug 29, 2023 at 8:24
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