I surely am missing something about the notion of connectedness, and I clarify this by means of an example:(adsbygoogle = window.adsbygoogle || []).push({});

O(n), the orthogonal group, has two subsets with detO=1 and detO=-1. Now, the maximally connected component of O(n) is SO(n), which is the subgroup with detO=1 including the Identity, while the other part is simply a coset (and not a subgroup, as it doesn't, of course, contain I).

Thus, O(n) is NOT a connected group.

I do not understand why, on the other hand, U(n) is said to be connected when it has got, in exactly the same way as O(n), two subsets with detU=1 and detU=-1, where we call the former SU(n).

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# Connectedness of Lie Groups

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