640:549 Lie Groups (Spring, 2005) -- Syllabus

Text: Wulf Rossmann, Lie Groups: An Introduction Through Linear Groups,
    ISBN 0-19-859683-9, Oxford University Press, New York, 2002.

Date Lecture Reading Topics
1/19 1 1.1 Vector Fields and one-parameter matrix groups
1/24 2 1.2 The exponential map and its differential
1/26 3 1.3 Campbell-Baker-Hausdorff series
1/31 4 2.1 Linear groups
2/02 5 2.1 Examples of linear groups
2/07 6 2.2 Lie algebra of a linear group
2/09 7 2.3 Exponential coordinates
2/14 8 2.3 Topology and analytic coordinates on linear groups
2/16 9 2.4 Connected linear groups
2/21 10 2.5 Lie algebra--Lie group correspondence
2/23 11 2.5 Classification of abelian Lie groups
2/28 12 2.5 Lie algebra--Lie group dictionary
3/02 13 2.5 Commutator subgroup, Homomorphisms
3/07 14 2.6, 2.7 Coverings of linear groups, Closed subgroups
3/09 15 3.1 Classical groups
    Spring Break  
3/21 16 3.1 Classical groups
3/23 17 3.1 Polar Decomposition of Classical Groups
3/28 18 4.1 Manifolds
3/30 19 4.2 Homogeneous spaces
4/04 20 4.2, 4.3 Homogeneous spaces and Lie groups
4/06 21 5.1 Integration on manifolds
4/11 22 5.2 Integration on Lie groups and homogeneous spaces
4/13 23 5.3 Conjugacy classes in U(n); Weyl's integral formula for U(n)
4/18 24 5.3, 6.1 Proof of Weyl's integral formula; Representations of compact groups
4/20 25 6.2 Schur's Lemma, Peter-Weyl theorem
4/25 26 6.3 Characters
4/27 27 6.4 Weyl's character formula for U(n)
5/02 28 6.5 Highest weight theorem for U(n)

Back to home page   of 640:549.


Roe Goodman / goodman "at" math "dot" rutgers "dot" edu / Revised April 17, 2005