Jordan pairs and bounded symmetric domains
These notes are based on a series of lectures given
at the University of California at Irvine in the spring of
1977. My main aim was to show how the theory of Jordan
algebras and, more generally, Jordan triple systems and
Jordan pairs, may be applied to study the geometry of
bounded symmetric domains.
I'm grateful to Irene Paniello for making these notes available in electronic
form.
TABLE OF CONTENTS
- Introduction
- Notations
- Bounded symmetric domains
- The Jordan pair associated with a bounded
symmetric domain
- Tripotents and Peirce decomposition
- Correspondence between bounded symmetric
domains and Jordan pairs; classification
- The manifold of tripotents
- The boundary of D
- The compactification of V
- The automorphism group of X
- G as a real algebraic group
- Cayley transformations and Siegel domain
realizations
- Real bounded symmetric domains
- Appendix
- Bibliography
O. Loos < ottmar.loos@fernuni-hagen.de >