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.
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