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[Lecture Notes in Mathematics] The Geometry of Jordan and Lie Structures Volume 1754 || Chapter IV: The classical spaces

✍ Scribed by Bertram, Wolfgang

Book ID
120394402
Publisher
Springer Berlin Heidelberg
Year
2000
Tongue
German
Weight
1020 KB
Edition
2000
Category
Article
ISBN
3540414266

No coin nor oath required. For personal study only.

✦ 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.

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