

Course: Math 744: Lie Groups I
Instructor: Professor Jeffrey Adams
Time: 1212:50
Location: Math 0102
Office Hours: M 12, F 1112
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. SpringerVerlag, New York, 1995 ISBN: 0387136789.
(Out of print)
 Lie groups by Daniel Bump.
SpringerVerlag, Graduate Texts in Mathematics, 225. 2004. ISBN: 0387211543
 Lie Groups, Lie Algebras, and Representations: An Elementary
Introduction by Brian C. Hall, Springer, Graduate Texts in
Mathematics, ISBN10 0387401229
 Compact Lie Groups by Mark Sepanski, Springer, GTM 235, 2000, ISBN10 0387302638.
 Linear Algebraic Groups by Tonny Springer, 2nd edition, Birkhauser 2009. ISBN: 9780817648398
 Lie groups and algebraic groups by Onishchik, A. L. and Vinberg, B. Springer Series in Soviet Mathematics. SpringerVerlag, Berlin, 1990. ISBN: 3540506144
 Very Basic Lie Theory by Roger Howe, Amer. Math. Monthly 90 (1983),
no. 9, 600623. Available through JSTOR
 Representation Theory: A First Course by William Fulton and Joe
Harris, Springer, Graduate Texts in Mathematics, ISBN10 0387974954.
 Lectures on Lie Groups by J. F. Adams,
University of Chicago Press, ISBN10: 0226005305, ISBN13: 9780226005300
v
 Introduction to Lie Algebras and Representation Theory by James E.
Humphreys, Springer, Graduate Texts in Mathematics, ISBN10:
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 46
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.
