The geometry of Jordan and Lie structures
By: Wolfgang Bertram.
Series: Lecture notes in mathematics -- 1754; Lecture notes in mathematics (Springer-Verlag) -- 1754.
Publisher: Springer
Published: 2000
Place of publication: Berlin; New York
Language: eng
Number of pages: 269
Subjects: Jordan algebras; Lie algebras
Description: 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.
Notes: Includes bibliographical references (p. [256]-262) and indexes.