Course: Math 744: Lie Groups I
Instructor: Professor Jeffrey Adams
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.
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.
- 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
- Introduction to Lie Algebras and Representation Theory by James E.
Humphreys, Springer, Graduate Texts in Mathematics, ISBN-10:
- 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
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.