The geometry of Jordan and Lie structures / Wolfgang Bertram.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 1754.Publisher: Berlin ; New York : Springer, ©2000Description: 1 online resource (xvi, 265 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540444589; 3540444580Report number: V1043227Subject(s): Jordan algebras | Lie algebras | Jordan algebras | Lie algebrasGenre/Form: Electronic books. Additional physical formats: Print version:: Geometry of Jordan and Lie structures.DDC classification: 510 s | 512/.24 LOC classification: QA3 | .L28 no. 1754 | QA252.5Online resources: Click here to access online
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Includes bibliographical references (pages 256-262) and indexes.
Jordan-lie functor -- Symmetric spaces and the lie-functor -- Prehomogeneous symmetric spaces and jordan algebras -- Jordan-lie functor -- Classical spaces -- Non-degenerate spaces -- Conformal group and global theory -- Integration of Jordan structures -- Conformal lie algebra -- Conformal group and conformal completion -- Liouville theorem and fundamental theorem -- Algebraic structures of symmetric spaces with twist -- Spaces of the first and of the second kind.
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.