Lie Groups (Universitext)

Rating:
Summary: A Brilliant Book on Lie Groups
Review: I have read this book with great interest. It deals with the theory of Lie groups from the global point of view, not only the usual Lie algebraic treatment. Of particular originality is the theory of orbits for compact groups, an issue with many applications such as the patterns of symmetry breaking in elementary particle physics. I also particularly appreciated the chapter about the Borel-Weil theory of representations which does not seem to be available in textbooks. The style and breadth of the exposition will certainly make it an instant classic, a perfect complement to the Lie algebra texts by Humphreys or Jacobson. I also appreciated the emphasis on the differential geometric aspects of the subject. One regret is that the authors did not delve into the orbit theory of complex Lie groups and the link with geometric invariant theory.

Rating:
Summary: A Brilliant Book on Lie Groups
Review: I have read this book with great interest. It deals with the theory of Lie groups from the global point of view, not only the usual Lie algebraic treatment. Of particular originality is the theory of orbits for compact groups, an issue with many applications such as the patterns of symmetry breaking in elementary particle physics. I also particularly appreciated the chapter about the Borel-Weil theory of representations which does not seem to be available in textbooks. The style and breadth of the exposition will certainly make it an instant classic, a perfect complement to the Lie algebra texts by Humphreys or Jacobson. I also appreciated the emphasis on the differential geometric aspects of the subject. One regret is that the authors did not delve into the orbit theory of complex Lie groups and the link with geometric invariant theory.