Introduction to Lie Groups I Prof. Alessandra Iozzi (E-Mail)   Course announcement Course Time: Thursday, 10-12 Place: Grosser Hörsaal, Mathematisches Institut Starting date: Thursday, 3rd November 2005. Exercise sessions Time: Every second Wednesday 14-16 Place: Grosser Hörsaal, Mathematisches Institut Starting date: Wednesday, 16th November 2005 Assistent: Philippe Bonnet (E-Mail) Prerequisites Linear algebra and basic notions about differential geometry. Content Definition, basic properties. Lie subgroups. Lie algebras and their relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's theorem, Engel's theorem. Definition of algebraic groups and relation with Lie groups. Applications: Lie groups in the diffeomorphism group of a manifold, invariant volume forms, invariant metrics. Ideas on: semisimple representations, Cartan decomposition, root space decomposition, Iwasawa decomposition. Intended audience Diploma students from the fifth semester on, beginning graduate students. References: A. Sagle & R. Walde, Introduction to Lie groups and Lie algebras, Academic Press, 1973 F. Warner, Foundations of differentiable manifolds and Lie groups, Springer, 1971 H. Samelson, Notes on Lie algebras, Springer, 1990 S.Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, 1978 A.Knapp, Lie groups, Lie algebras and cohomology", Princeton University Press) Exercise sheets Exercises will be assigned at first during the lectures. On the Thursday of the week in which there is no exercise session an exercise sheet will be handed out. Exercises are to be handed in to Philippe Bonnet on the following Monday and will be discussed during the exercise session on Wednesday. Sheet 1, due on Nobvember 14th, pdf or ps Sheet 2, due on November 28th, pdf or ps Sheet 3, due on December 12th, pdf or ps Sheet 4, due on January 23rd, pdf or ps Sheet 5, due on February 6th, pdf or ps

Last modification: 28th Jan. 2006