OXFORD C3.5 LIE GROUPS 2013-2014
Prof. Alexander F. Ritter, Associate Professor, University of Oxford.
LECTURE NOTES AND EXERCISES
♦ All Lecture Notes in one large PDF file
♦ All Lecture Notes in one large PDF file (2 pages per side)
♦ All Question Sheets in one PDF file
♦ Lecture 01: Definition of Lie group, Crash course on Manifolds
♦ Lecture 02: Examples of Lie groups, Lie algebra of G
♦ Lecture 03: Flows, One-parameter subgroups
♦ Lecture 04: The exponential map
♦ Lecture 05: Lie group homs, Lie algebra homs, Adjoint maps Ad and ad
♦ Lecture 06: adjoint representation, classification of abelian Lie groups
♦ Lecture 07: Lie subgroups, Lie subalgebras
♦ Lecture 08: Closed subgroups, continuous homomorphisms
♦ Lecture 09: Subgroup-subalgebra correspondence (Chevalley)
♦ Lecture 10: Covering spaces, Lie alg homs vs Lie gp homs, Lie's third theorem
♦ Lecture 11: Representation theory
♦ Lecture 12: Compact G: complete reducibility, orthogonality relations
♦ Lecture 12: Optional non-examinable: integration on compact G
♦ Lecture 13: R(G), Cl(G), F(G), Peter-Weyl theorem
♦ Lecture 14: Handout 1: Representation theory of circle and torus
♦ Lecture 14: Handout 2: Roots for matrix groups
♦ Lecture 14: Maximal tori in compact Lie gps
♦ Lecture 15: The Weyl group, representations of U(n)
♦ Lecture 16: Reflections, Killing form, Classification of compact Lie gps
♦ Question sheet 1
♦ Question sheet 2
♦ Question sheet 3
♦ Question sheet 4
♦ Question sheet 5
♦ Question sheet 6
___________________________
Prof. Alexander F. Ritter. Contact
me.
Associate Professor in Geometry, Mathematical Institute, Oxford.
The Roger Penrose Fellow and Tutor, Wadham College, Oxford.