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.