Instructor: Debra Lewis
Office: 359B Baskin Engineering
Phone: 459-2718
E-mail: lewis at ucsc dot edu
(checked more often than voicemail or gmail)
and/or DebraKLewis at gmail dot com
Lecture: MW 10:00-11:45, 360 JBE
Office hours: TBA
Course web page: http://people.ucsc.edu/~lewis/Math227
(here)
Lie Groups, J.J. Duistermaat and J.A.C. Kolk, Springer.
Possible supplementary texts:
Lie Groups and Algebra with Applications to Physics, Geometry, and Mechanics, D.H. Sattinger and O.L. Weaver, Springer.
Matrix Groups, Morton L. Curtis, Springer.
A Survey of Lie Groups and Lie Algebras with Applications and
Computational Methods, Johan G.F. Belinfante and Bernard Kolman, SIAM.
VERY TENTATIVE SCHEDULE
| Monday | Wednesday |
| January 9: classical matrix groups and algebras | |
| January 14: Lie groups and algebras, the adjoint action | January 16: the exponential map |
| January 21: HOLIDAY | January 23: Lie's three theorems |
| January 28: Lie's three theorems (cont.) | January 30: Lie subgroups |
| February 4: actions and quotients | February 6: compact Lie groups, centralizers |
| February 11: roots and root spaces | February 13: maximal tori |
| February 18: HOLIDAY | February 20: the Weyl group |
| February 25: orbit structure | February 27: the fundamental group |
| March 3: representations | March 5: Shur's lemma |
| March 10: averaging | March 13: matrix coefficients and characters |
| March 17: Peter-Weyl theorem |