Groupes et algèbres de Lie.

Université de Rennes 1, printemps 2001.


These are notes for a course given at Rennes at the DEA level, for students in algebra and geometry, or in analysis, or in probability theory. The notes are based on a handwritten version of about 128 pages by Dominique Cerveau, who has taught the same course during the last few years, and who is of course not responsible for the mistakes in this version. The main result of the course seems to be the Peter-Weyl theorem, which is a generalisation of Fourier theory on the circle to compact Lie groups. I will try to follow his notes quite faithfully, but also I would like to put a little bit more emphasis on representations of Lie groups, with of course the explicit examples for the groups SO3 and SU2. In particular, I would like to find time to discuss the applications of these examples to quantum mechanics (possibly also the relation between SU3 and quarks. The course takes place in 30 hours (10 weeks, 3 hours a week). One reason to type these notes is to have them available on the internet, in a convenient format.

During the course, I will write up what I am doing. So at the end of March these notes should be complete.

fichier PostScript comprimé;/compressed PostScript file (262 kB)

fichier pdf (777 kB)

Retour à mes polycopiés, etc.

Dernière modification: 31/05/2001