The Geometry of Jordan and Lie Structures

Wolfgang Bertram (eds.)3540414266, 9783540414261

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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Table of contents :
Chapter I: Symmetric spaces and the Lie-functor….Pages 1-41
Chapter II: Prehomogeneous symmetric spaces and Jordan algebras….Pages 42-60
Chapter III: The Jordan-Lie functor….Pages 61-80
Chapter IV: The classical spaces….Pages 81-96
Chapter V: Non-degenerate spaces….Pages 97-115
Chapter VI: Integration of Jordan structures….Pages 116-126
Chapter VII: The conformal Lie algebra….Pages 127-142
Chapter VIII: Conformal group and conformal completion….Pages 143-170
Chapter IX: Liouville theorem and fundamental theorem….Pages 171-183
Chapter X: Algebraic structures of symmetric spaces with twist….Pages 184-215
Chapter XI: Spaces of the first and of the second kind….Pages 216-239
Chapter XII: Tables….Pages 240-253
Chapter XIII: Further topics….Pages 254-255