What would be your suggestion of textbooks in Lie groups and Galois theory? - MathOverflow [closed]

What would be your suggestion of textbooks in Lie groups and Galois theory?

2010-08-17T06:30:29Z

Possible Duplicate:
Learning about Lie groups

Actually, I'm having the hard time with Serre's book on Lie groups and algebras: the lack of motivation is my biggest problem. So, what would you suggest for a first, illustrative, but systematic and deep course on Lie groups? The lack of good books on Galois theory on my way is a different problem: too much formalism without much of results is what I've seen in Postnikov's "Galois theory" so far

As a little note on preferences: right now I'm enjoying the topology book of Seifert and Threlfall(with its geometric illustrations) and homological algebra by Cartan & Eilenberg(because of the well-understandable language of diagrams).

Answer by Sheikraisinrollbank for What would be your suggestion of textbooks in Lie groups and Galois theory?

2010-08-17T10:04:35Z

Frank Warner's book "Foundations of differentiable manifolds and Lie groups" is one of the standards. You can't go wrong by looking at Chevalley's book "Theory of Lie groups" or Weyl's (classic, of course) "The classical groups: their invariants and representations". Knapp's big book "Lie groups: beyond an introduction" has lots (and lots) of information.

Answer by Benoît Kloeckner for What would be your suggestion of textbooks in Lie groups and Galois theory?

2010-08-17T10:19:06Z

Concerning Lie groups and Lie algebra, I suggest Knapp's "Lie groups, beyond an introduction". It starts with a chapter 0 on classical matrix groups, then goes on to the general theory.

Answer by pi2000 for What would be your suggestion of textbooks in Lie groups and Galois theory?

2010-08-17T11:40:20Z

1.Lie Groups: M.Postnikov Lie Groups and Lie Algebras-vol5 of his Lectures in Geometry; as a bonus not systematic but deep and witty: Roger Godement-Introduction à la théorie des groupes de Lie(french)

2.Galois Theory: H.M Edwards -Galois Theory Not much "abstract nonsense", with historical insight

V.B. Alekseev-Abel's Theorem In Problems And Solutions: Based on the lectures of Professor V.I.Arnold

Answer by Anthony Pulido for What would be your suggestion of textbooks in Lie groups and Galois theory?

2010-08-17T12:02:22Z

Ian Stewart's Galois Theory is a nice introductory text to Galois theory. Recently, however, I've been doing exercises from chapters 13 and 14 from Abstract Algebra by Dummit and Foote. This might be a faster introduction. Joseph Rotman's short book Galois Theory is also introductory, but fast and very readable.

Answer by Tim Porter for What would be your suggestion of textbooks in Lie groups and Galois theory?

2010-08-17T12:09:47Z

As always it depends on what you know (i.e. your background) and on what you need. For Galois theory, there is a nice book by Douady and Douady, which looks at it comparing Galois theory with covering space theory etc. Another which has stood the test of time is Ian Stewart's book.

For Lie groups and Lie algebras, it can help to see their applications early on, so some of the text books for physicists can be fun to read. They skip some detail but provide the intuition that is sometimes lacking in purely mathematical texts.

Answer by Somnath Basu for What would be your suggestion of textbooks in Lie groups and Galois theory?

2010-08-17T15:09:10Z

Patrick Morandi's Field and Galois Theory is a good book for beginners. He gives lots of examples and has interesting exercises too. For a later reading though, I would suggest the Galois theory section in Lang's Algebra.

I really liked Hsiang's Lectures in Lie Groups although it may be a bit short for a full course. And Kirillov Jr.'s book Introduction to Lie Groups and Lie Algebras (also available as a published book) is a very good introduction to the topic with plenty of nice examples in the exercises. And lastly, Serre's Complex Semisimple Lie Algebras is great once you manage to get through it, i.e., it's a gem but not for the first reading!