There are several books on "Lie Groups". I confused to select a book for study due to lack of some background. I have never did thoroughly reading course on manifolds, and so the books on Lie algebra, which include this topic in introduction I do not read immediately.

At the same time, I wonder whether it is possible to study Lie groups with almost no knowledge of manifold theory. (For example, to study $p$-group, it is not necessary to study a book of Group Theory first, in my opinion, since lot of theorems on general finite groups are trivial for $p$-groups!)

Some books by experts in the subject start with tangent space, tangent bundles, and then I immediately keep the book aside - because I do not have basic knowledge of the subject.

Thus, I want to see some lecture notes or books on Lie groups which require very less "analysis/manifold theory" prerequisite.

The book/notes I will follows is with respect to following things to understand.

(1) Basic and important "concrete" examples of Lie groups over $\mathbb{R},\mathbb{C}$ with some detailed illustration that "they are lie groups"

(2) abstract analogous of Lie groups (i.e. over arbitrary fields).

(3) Their connection with Lie algebra.

(4) Some overview of Chevalley's and Steinberg's research work on simple Lie groups.

Q. Can one suggest good source of notes/books on Lie groups with less requirement on "analysis/manifold theory"?

  • 2
    $\begingroup$ Stillwell's book doesn't assume any background in differential geometry. $\endgroup$ – anon Nov 20 '17 at 5:16

Most Lie groups one meets can be treated as matrix groups. Certainly all compact Lie groups can be. If you restrict your attention to these, you can do away with all the machinery of manifold theory. One accessible textbook I know that does this is the one by Hall. Also any of numerous Lie groups for physicists textbooks would serve, such as Cornwall or Tung.


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