Prof. Alexander F. Ritter, Associate Professor, University of Oxford.

♦ 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

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Prof. Alexander F. Ritter. Contact me.

Associate Professor in Geometry, Mathematical Institute, Oxford.

The Roger Penrose Fellow and Tutor, Wadham College, Oxford.