Geometry of Lie Groups

Description

Title page Contents (detailed) Preface Chapter 0. Structures of Geometry 0.1. Algebraic Structures 0.2. Topological Structures 0.3. Order Structures 0.4. Incidence Structures 0.5. Metric Structures 0.6. Tensors and Linear Operators 0.7. Riemannian Manifolds and Manifolds with Affine Connections 0.8. Topological Groups and Lie Groups Chapter I. Algebras and Lie Groups 1.1. Commutative Associative Algebras 1.2. Noncommutative Associative Algebras 1.3. Alternative Algebras 1.4. Lie Algebras and Lie Groups 1.5. Jordan and Elastic Algebras 1.6. Linear Representations of Simple Lie Groups Chapter II. Affine and Projective Geometries 2.1. Affine Geometries 2.2. Projective Geometries 2.3. Affine and Projective Transformations 2.4. Lines, m-Planes, and Hyperplanes 2.5. Hyperquadrics 2.6. Linear Complexes 2.7. Projective Configurations 2.8 Symmetry and Parabolic Figures 2.9. Finite Geometries Chapter III. Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries 3.1. Euclidean and Pseudo-Euclidean Spaces 3.2. Motions and Similitudes 3.3. Lines, m-Planes and Hyperplanes 3.4. Polyhedra 3.5. Hyperquadrics 3.6. Hyperspheres 3.7. Sliding Vectors 3.8. Conformal and Pseudoconformal Spaces 3.9. Finite Geometries 3.10. Applications to Physics Chapter IV. Elliptic, Hyperbolic, Pseudoelliptic, and Pseudo-hyperbolic Geometries 4.1. Elliptic, Hyperbolic, Pseudoelliptic, and Pseudohyperbolic Spaces 4.2. Motions 4.3. Lines, m-Planes and Hyperplanes 4.4. Interpretations of Quadratic and Hermitian Spaces 4.5. Trigonometry 4.6. Sectional Curvature in Hermitian Spaces 4.7. Polyhedra, Hyperquadrics, and Hyperspheres 4.8. Interpretations of Skopets and Popovic 4.9. Regular Polyhedra and Honeycombs 4.10. Symmetry and Parabolic Figures 4.11. Space Forms 4.12. Sliding Vectors 4.13. Finite Geometries 4.14. Applications to Physics Chapter V. Quasielliptic, Quasihyperbolic, and Quasi-Euclidean Geometries 5.1. Quasielliptic, Quasihyperbolic, and Quasi-Euclidean Spaces 5.2. r-Quasielliptic, r-Quasihyperbolic, and r-Quasi-Euclidean Spaces 5.3. Hyperquadrics, Hyperspheres, and Hypercycles 5.4. Lines, m-Planes and Symmetry Figures 5.5. m-Horospheres in Pseudoelliptic and Pseudohyperbolic Spaces 5.6. Sliding Vectors 5.7. Quasi-Riemannian, Quasipseudo-Riemannian, r-Quasi-Riemannian, and r-Quasipseudo-Riemannian Manifolds and Symmetric Spaces 5.8. Applications to Physics Chapter VI. Symplectic and Quasisymplectic Geometries 6.1. Symplectic Spaces 6.2. Interpretations of Symplectic Spaces 6.3. Quasisymplectic and r-Quasisymplectic Spaces 6.4. Symmetry and Parabolic Figures 6.5. Symplectic and Quasisymplectic Connections 6.6. Finite Geometry 6.7. Applications to Physics Chapter VII. Geometries of Exceptional Lie Groups. Metasymplectic Geometries 7.1. Geometry of the Groups G₂ 7.2. Geometry of the Groups F₄ and E₆ 7.3. Geometry of the Groups E₆, E₇, and E₈ 7.4. Symplectic and Metasymplectic Geometries 7.5. Symmetry Figures and Symmetric Spaces 7.6. Parabolic Figures and Fundamental Representations 7.7. Finite Geometries 7.8. Applications to Physics References Index of Persons Index of Subjects