Wikipedia webpage https://en.wikipedia.org/wiki/Simple_Lie_group contains a full list of all simple (centerless) real Lie groups. One of the columns in tables (therein) contains fundamental groups of these Lie groups, or - in other words - the centers of their universal covers. I wonder where I can find information on these centers. I'm aware of an old paper by Sirota and Solodovnikov [Noncompact semisimple Lie groups, Russian Mathematical Surveys, 1963, Volume 18, Issue 3, 85-140], which would be enough for me, but - according to Freudenthal's (!) review in Mathematical Reviews - their article contains a number of errors. Moreover, description of the centers given in that paper (or, to be more precise, in its English translation) is incompatible with the list on the aforementioned Wikipedia webpage. (For example, in this translation one finds that the center of the simply connected Lie group whose Lie algebra is split of type E6 is infinite cyclic, which is surely false, because a maximal compact subgroup of its centerfree `version' is semisimple). Could anyone help me and give any reference to the above topic (i.e., centra of simply connected simple real Lie groups)? (I'm mostly interested in books/articles/etc. written in English, but if no such exist, any other will also be acceptable).
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$\begingroup$ There's a table in H. Gündogan, "The Component Group of the Automorphism Group of a Simple Lie Algebra and the Splitting of the Corresponding Short Exact Sequence" Journal of Lie Theory Volume 20 (2010) 709–737 (see p718) heldermann-verlag.de/jlt/jlt20/guendola2e.pdf $\endgroup$– YCorCommented Mar 4 at 19:11
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1$\begingroup$ I don't find there any table with the centers of, e.g., non-compact non-complex simple Lie algebras. No column of the table on page 718 (in the Gundogan's paper) deals with these centers (e.g., the center of E6(-14) is infinite cyclic - there is no such group in this table). $\endgroup$– PiotrCommented Mar 4 at 20:34
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$\begingroup$ Oops, you're right, I checked but not carefully... $\endgroup$– YCorCommented Mar 4 at 22:39
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