Cartanfaktoren, reelle Formen und ihre Strukturgruppen (Cartan factors, real forms and their structure groups)

The structure group of a complex JB*-triple U is a complex Lie group which properly contains the automorphism group and carries a natural conjugation. A real JB*-triple E is a real form of U, i.e. the fix point set of a conjugation.

It is shown that such a conjugation on U induces a conjugation on the structure group of U which commutes with the natural conjugation. The respective fix point sets are the automorphism group of U and the structure group of E. This result is used to explicitly determine the structure groups of the non-exceptional real and complex cartan factors.

This Diplom Thesis is written in German. The first three chapters contain well known material on JB-triples and Cartan factors (struktur_1.dvi). In chapters 4 and 5 much attention is given to real Cartan factors and their isometry groups. Detailed proofs of [Kaup: On real Cartan Factors (1997)] are given (struktur_2.dvi). Chapter 6 contains the results described above (struktur_3.dvi).

F. Lutscher <frithjof.lutscher@uni-tuebingen.de>