
Linear Lie Groups
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Content
- Front Cover
- Linear Lie Groups, Volume 35
- Copyright Page
- Contents
- 0. Introduction
- 0.0 Preface
- Chapter 0.1-7. On Notation and Nomenclature
- 0.1. Logical Symbols
- 0.2. Set Theory Symbols
- 0.3. Topological Symbols
- 0.4. Algebraic Symbols
- 0.5. Analytic Symbols
- 0.6. Logograms
- 0.7. Nomenclature
- Chapter 1-5. Preliminaries
- 1. Complex Extension, Real Restriction, and Waiving
- 2. The Exponential
- 3. Some Lie Groups
- 4. Topological Groups
- 5 . Differentiable Mappings
- Chapter 6-12. The Connection between Local Linear Lie Groups and Lie Algebras
- 6. Definition of Local and Global Linear Lie Groups
- 7. The Infinitesimal Algebra of a Local Linear Lie Group
- 8. The Exponential Presentation
- 9. Homomorphisms, Automorphisms, and Derivations
- 10. Expanding Linear Lie Algebras and Their Homomorphisms into Linear Lie Groups and Their Local Homomorphisms
- 11. Dropping Differentiability Assumptions
- 12. Subgroups and Subalgebras, Normal Subgroups and ldeals
- Chapter 13-19. Solvability and Semisimplicity
- 13. Solvable Groups and Solvable Lie Algebras
- 14. Invariants of Linear Lie Groups and Algebras
- 15. Roots and Rank
- 16. Important Classes of Complex Lie Algebras
- 17. Solvable Subalgebras
- 18. Cleaving
- 19. Semisimplicity
- Chapter 20-27. Dressings and Classification of Semisimple Complex Lie Algebras
- 20. The First Dressing of Complex Semisimple Lie Algebras
- 21. The First Weyl Norming and the Second Dressing of Complex Semisimple Lie Algebras
- 22. G Determined by W*
- 23. The Second Weyl Norming and the Third Dressing of Complex Semisimple Lie Algebras
- 24. The Unitary and Standard Restrictions of a Semisimple Lie Algebra
- 25. G Determined by W++
- 26. Classification of Semisimple Complex Lie Algebras Up to Isomorphism
- 27. G2 and F4. The Chevalley Dressing
- Chapter 28-38. Topological and Integration Methods
- 28. Homotopy and Wrapping
- 29. Fundamental Groups and Wrappings of Topological Groups
- 30. Compactness Aspects of Semisimple and Abelian Groups
- 31. The Conjugacy Theorem for Centerfree Unitarily Restricted Semisimple Lie Groups
- 32. The Fundamental Group of Centerfree Unitarily Restricted Semisimple Groups
- 33. The Automorphisms of Semisimple Lie Groups
- 34. Integration in Compact Groups
- 35. The Conducibility Theorem
- 36. Orthogonality Relations
- 37. The Characters of Compact Groups
- 38. Some Global Properties of Semisimple Linear Lie Groups
- Chapter 39-50. The Algebraic Approach to Linear Representations
- 39. The Associative Envelope of a Lie Algebra
- 40. The Casimir Tool
- 41. Weights and Integral Forms
- 42. Source, Top Weight, and Limitation of a Representation
- 43. Finite-Dimensional Irreducible Representations
- 44. The Construction of All Finite-Dimensional Representations
- 45. The Fundamental Weights
- 46. The Fundamental Group of Unitarily Restricted Semisimple Lie Groups
- 47. Weyl's Character and Dimension Formula
- 48. Algebraic Proof of Weyl's Formulas
- 49. Clifford Algebras and Spin Representations
- 50. The Conducibility Theorem (Algebraically Proved) and E. E. Levi's Theorem
- Chapter 51-62. Reality in Lie Groups and Algebras and Their Linear Representations
- 51. Maximally Compact Dressing
- 52. Classification of Inner Types
- 53. Classification of Outer Types
- 54. Further Remarks on Real Classification
- 55. Contravalence and Virtual Reality of Linear Representations
- 56. Contravalence of Weights
- 57. Self-Contravalence
- 58. Computing e for Simple Lie Algebras
- 59. Invariant Bilinear and Sesquilinear Forms
- 60. Minimally Compact Dressing
- 61. Real Semisimple Linear Lie Groups as Products of Maximal Compact and Solvable Groups
- 62. The Fundamental Groups of the Real Types
- Chapter 63-67. Symmetric Spaces
- 63. Homogeneous Spaces and Riemannian Manifolds-A Sketch
- 64. Symmetric Spaces
- 65. Minimal and Maximal Symmetric Spaces
- 66. Autometrisms of Symmetric Spaces, Automorphisms of Real Semi- simple Lie Groups
- 67. Fundamental Groups of Symmetric Spaces
- Chapter 68-75. Tits Geometries
- 68. A List of Fundamental Theorems
- 69. Proofs of the Statements of Section 68
- 70. Introduction of Incidence Geometries of Semisimple Lie Groups 70.20. The Special Case of rank 2
- 71. An Axiomatic Approach to Incidence Geometries of Semisimple Lie Groups
- 72. Covariants of Pairs of Elements in Incidence Geometries of Semisimple Groups
- 73. The Classes of Pairs of Elements in an F4-Geometry
- 74. The Incidence Geometries of Real Semisimple Lie Groups
- 75. C-Graphs of Incidence Geometries of Simple Semisimple Lie Groups
- Chapter 76-77. Betti Numbers of Semisimple Lie Groups and Regular Subalgebras of Semisimple Lie Algebras
- 76. ad-Nilpotents and Semisimple Subalgebras of Rank 1
- 77. Killing-Coxeter Tools, Betti Numbers
- Appendix
- Table A. The Graph and Dimension of G e Alg Lie Com SSS
- The Length Square of the Shortest Nonzero Rootform
- Table B. The Positive Rootforms on a Natural Basis
- Table C. The Positive Rootforms on a Symmetric Basis and Their Altitudes
- Table D. Number of Rootforms of Given Positive Altitude a
- Table E. Dominant Rootforms
- Table F. Fundamental Weights
- Table G. Isomorphisms and Equivalences for Low-Rank Semisimple Lie Algebras
- Key to Definitions
- Author Index
- Pure and Applied Mathematics
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