The Geometry of Jordan and Lie Structures

First Part: The Jordan-Lie functorI.Symetric spaces and the Lie-functor1. Lie functor: group theoretic version2. Lie functor:differential geometric version3. Symmetries and group of displacements4. The multiplication map5. Representations os symmetric spaces6. ExamplesAppendix A: Tangent objects and their extensionsAppendix B: Affine ConnectionsII. Prehomogeneous symmetric spaces and Jordan algebras1. Prehomogeneous symmetric spaces2. Quadratic prehomogeneous symmetric spaces3. Examples4. Symmetric submanifolds and Helwig spacesIII. The Jordan-Lie functor1. Complexifications of symmetric spaces2. Twisted complex symmetric spaces and Hermitian JTS3. Polarizations, graded Lie algebras and Jordan pairs4. Jordan extensions and the geometric Jordan-Lie functorIV. The classical spaces1. Examples2. Principles of the classificationV. Non.degenerate spaces1. Pseudo-Riemannian symmetric spaces2. Pseudo-Hermitian and para-Hermitian symmetric spaces3. Pseudo-Riemannian symmetric spaces with twist4. Semisimple Jordan algebras5. Compact spaces and dualitySecond Part: Conformal group and global theoryVI. Integration of Jordan structures1. Circled spaces2. Ruled spaces3. Integrated version of Jordan triple systemsAppendix A: Integrability of almost complex structuresVII. The conformal Lie algebra1. Euler operators and conformal Lie algebra2. The Kantor-Koecher-Tits construction3. General structure of the conformal Lie algebraVIII. Conformal group and conformal completion1. Conformal group: general properties2. Conformal group: fine structure3. The conformal completion and its dual4. Conformal completion of the classical spacesAppendix A: Some identities for Jordan triple systemsAppendix B: Equivariant bundles over homogeneous spacesIX. Liouville theorem and fundamental theorem1. Liouville theoremand and fundamental theorem2. Application to the classical spacesX. Algebraic structures of symmetric spaces with twist1. Open symmetric orbits in the conformal completion2. Harish-Chandra