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I studied algebra and group theory at the university about 20 years ago. Lately I've been reading the occasional maths book/article and they mention things like $\rm{SO}(n)$ and $\rm{SU}(2)$ as classes of groups.

I can see each of these are different categories of groups and remember studying these individually, however it seems these categories mean more now and are a part of some larger theory.

If this is the case, if someone could point me towards a reference / book (kindle would be good) it would be appreciated.


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I suggest that you read the Wikipedia page on Lie groups and have a look at the references given there. Your examples $\operatorname{SU}(n)$ and $\operatorname{SO}(n)$ are compact Lie groups. Personally, I found the notes by Hilgert and Neeb quite good (link goes to a pdf on Hilgert's homepage), but they may be a bit advanced. – t.b. May 7 '11 at 13:51
@t.b. The link is broken, teebee. :( – Ravi Aug 5 '12 at 10:45
@FortuonPaendrag: yes, these notes were published as a Springer Monograph in Mathematics and subsequently removed from the homepage. Google books link: Hilbert, Neeb, Structure and Geometry of Lie groups. – t.b. Aug 5 '12 at 11:15
HilGert :) ${}{}$ – t.b. Aug 5 '12 at 11:38
up vote 3 down vote accepted

What you're looking for is the theory of Lie groups. There are many books about this at different levels of sophistication. Perhaps a good place to begin is Stillwell's book Naive Lie Theory.

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Many thanks, I've been meaning to read about these as well :-) – daven11 May 7 '11 at 13:59

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