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featured Lie-groups Lie-algebra books

shared by arithwsun arithwsun on 07 Jan 09 - Cached
  • Hall, Brian C. Lie groups, Lie algebras, and representations. An elementary introduction. Graduate Texts in Mathematics, 222. Springer-Verlag, New York, 2003. This is only a recommended text, but it is highly recommended. By emphasizing matrix groups, the book covers most of the important examples occuring in nature while avoiding a lot of the technical difficulties necessary in a more general treatment. It gives an excellent presentation of most of what we'll talk about. I think it will be a great book to read to supplement the lectures. Looking around on the web, I found many copies that were very reasonably priced.
  • Humphreys, James E. Introduction to Lie algebras and representation theory. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978. A classic. Would have been my choice for a textbook, but unfortunately only covers Lie algebras.
  • Fulton, William; Harris, Joe. Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991. A beautiful book to read. Very useful for self-study. Bump, Daniel. Lie groups. Graduate Texts in Mathematics, 225. Springer-Verlag, New York, 2004. Perhaps too hard for beginners, but it contains an excellent collection of topics in the final part.
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  • Varadarajan, V. S. Lie groups, Lie algebras, and their representations. Graduate Texts in Mathematics, 102. Springer-Verlag, New York, 1984. Another classic. Very comprehensive. Representation theory of Lie groups. Proceedings of the SRC/LMS Research Symposium held in Oxford, June 28--July 15, 1977. Edited by G. L. Luke. London Mathematical Society Lecture Note Series, 34. Cambridge University Press, Cambridge-New York, 1979. See especially the articles by Macdonald and Bott.
  • Onishchik, A. L.; Vinberg, E. B. Lie groups and algebraic groups. Translated by D. A. Leites. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1990. Written with a more algebraic flavor. Takes the unusual approach of omitting almost all proofs and presenting the material as a series of exercies. (This is not as crazy as it sounds. In fact it's a very pleasant read.)
  • Knapp, Anthony W. Lie groups beyond an introduction. Second edition. Progress in Mathematics, 140. Birkhauser Boston, Inc., Boston, MA, 2002. Contains a lot of material with complete proofs. Thorough, but difficult to read if this is your first exposure. Springer, T. A. Linear algebraic groups. Second edition. Progress in Mathematics, 9. Birkhauser Boston, Inc., Boston, MA, 1998. Sure, it's a textbook on algebraic groups, but there's plenty of relevance for the study of Lie groups. Freudenthal, Hans; de Vries, H. Linear Lie groups. Pure and Applied Mathematics, Vol. 35 Academic Press, New York-London 1969. Bizarre and fascinating.
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