Math 744: Lie Groups

Fall 2014

Course: Math 744: Lie Groups I
Instructor: Professor Jeffrey Adams
Time: 12-12:50
Location: Math 0102
Office Hours: M 1-2, F 11-12

I'm going to be teaching the material from a combination of three viewpoints: compact groups, algebraic groups, and complex groups.

I wont' be using a single textbook. Here are some recommended references.

  • Lie Groups: An Introduction Through Linear Groups by Wulf Rossmann, Oxford Graduate Texts in Mathematics, Number 5 (out of print)
  • Representations of compact Lie groups by Brocker, Theodor and tom Dieck, Tammo. Graduate Texts in Mathematics, 98. Springer-Verlag, New York, 1995 ISBN: 0-387-13678-9. (Out of print)
  • Lie groups by Daniel Bump. Springer-Verlag, Graduate Texts in Mathematics, 225. 2004. ISBN: 0-387-21154-3
  • Lie Groups, Lie Algebras, and Representations: An Elementary Introduction by Brian C. Hall, Springer, Graduate Texts in Mathematics, ISBN-10 0387401229
  • Compact Lie Groups by Mark Sepanski, Springer, GTM 235, 2000, ISBN-10 0-387-30263-8.
  • Linear Algebraic Groups by Tonny Springer, 2nd edition, Birkhauser 2009. ISBN: 978-0-8176-4839-8
  • Lie groups and algebraic groups by Onishchik, A. L. and Vinberg, B. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1990. ISBN: 3-540-50614-4
  • Very Basic Lie Theory by Roger Howe, Amer. Math. Monthly 90 (1983), no. 9, 600--623. Available through J-STOR
  • Representation Theory: A First Course by William Fulton and Joe Harris, Springer, Graduate Texts in Mathematics, ISBN-10 0387974954.
  • Lectures on Lie Groups by J. F. Adams, University of Chicago Press, ISBN-10: 0226005305, ISBN-13: 978-0226005300 v
  • Introduction to Lie Algebras and Representation Theory by James E. Humphreys, Springer, Graduate Texts in Mathematics, ISBN-10: 0387900535
  • Lie Groups, an approach through invariants and representations by Claudio Procesi.
  • Three preprints by John Milne, at: Affine Group Schemes; Lie Algebras; Lie Groups; Reductive Groups; Arithmetic Subgroups
  • Lie Algebras and Representation Theory by Jim Humphreys
  • Bourbaki Lie Groups and Lie Algebras, Chapters 4-6
I recommend: The Greatest Mathematical Paper of All Time by A.J. Coleman, about Killing's 1888 paper on Lie algebras and root systems. There is also an interesting followup A Centennial: Wilhelm Killing and the Exceptional Groups by Sigurdur Helgason.

Terence Tau has a concise description of the classification of complex Lie Algebras on his blog.

There will be several problem sets assigned during the semester.