Lie groups
Lie groups
3-4 hours of lectures per week.
Most of the groups that you have encountered until now, have actually been Lie groups. As examples we mention the real numbers, the group 0(3) of rotations of
, the group of rigid mations of , the Lorentz- and the Poincarè groups from mathematical physics, the Heisenberg group from the theory of wavelets etc. As demonstrated by the examples, Lie groups play an important role as symmetry groups in many connections.In this course we will study the basic general theory of Lie groups. In part, this will be achieved by studying an important related vector space, the Lie algebra of a Lie group. Lie algebras and Lie groups are related via the exponential map.
The course will provide a good background for further studies, not just in Lie groups, but also in many other mathematical fields: representation theory of groups and algebras, differential geometry, and harmonic analysis to name a few. The topic is an active area of research.
The course will be continued in the Spring term of 2001. The reader who wants to get an impression of the subject, can consult the text book by Warner or, e.g., the monographs V. S. Varadarajan: "Lie groups, Lie algebras, and their representations." Prentice-Hall, Inc. 1974 and O. A. Barut and R. Raczka: "Theory of group representations and applications." PWN - Polish Scientific Publishers. Warszawa 1977.