[Lecture Notes in Mathematics] The Geometry of Jordan and Lie Structures Volume 1754 || Chapter IX: Liouville theorem and fundamental theorem

✍ Scribed by Bertram, Wolfgang

• Book ID: 120394405
• Publisher: Springer Berlin Heidelberg
• Year: 2000
• Tongue: German
• Weight: 930 KB
• Edition: 2000
• Category: Article
• ISBN: 3540414266
• DOI: 10.1007/3-540-44458-0_9

✦ Synopsis

The geometry of Jordan and Lie structures tries to answer the following question: what is the integrated, or geometric, version of real Jordan algebras, - triple systems and - pairs? Lie theory shows the way one has to go: Lie groups and symmetric spaces are the geometric version of Lie algebras and Lie triple systems. It turns out that both geometries are closely related via a functor between them, called the Jordan-Lie functor, which is constructed in this book.
The reader is not assumed to have any knowledge of Jordan theory; the text can serve as a self-contained introduction to (real finite-dimensional) Jordan theory.