- Title Pages
- Dedication
- Foreword
- Acknowledgments
- Part I Fundamental Concepts
- 0 Introduction
- 1 Parallelizable Manifolds
- 2 The Nonlinear Curvature
- 3 Local Lie Groups
- 4 The Centralizer
- 5 <i><span xml:lang="ell">ε</span></i>-Invariance
- 6 The Linear Curvature
- 7 The Structure Object
- Part II Some Consequences
- 8 The Nonlinear Spencer Sequence
- 9 Deformations
- 10 The de Rham Cohomology of an LLG
- 11 The Linear Spencer Sequence
- 12 The Secondary Characteristic Classes
- 13 The Homogeneous Flow
- 14 The Van Est Theorem
- 15 The Symmetry Group
- Part III How to Generalize?
- 16 Klein Geometries
- 17 The Universal Jet Groupoids
- 18 Embeddings of Klein Geometries into Universal Jet Groupoids
- 19 The Definition of a Prehomogeneous Geometry (PHG)
- 20 Curvature and Generalized PHGs
- Appendix Torsion-Free Connections
- References
- Index
The Symmetry Group
The Symmetry Group
- Chapter:
- (p.125) 15 The Symmetry Group
- Source:
- An Alternative Approach to Lie Groups and Geometric Structures
- Author(s):
Ercüment H. Ortaçgil
- Publisher:
- Oxford University Press
This chapter, which ends Part II on some consequences of the new approach, introduces an alternative prolongation theory of Klein geometries that is more geometric and intuitive than the well-known prolongation theory of a linear Lie algebra developed by Guillemin, Singer, and Sternberg.
Keywords: prolongation, normalizer
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- Title Pages
- Dedication
- Foreword
- Acknowledgments
- Part I Fundamental Concepts
- 0 Introduction
- 1 Parallelizable Manifolds
- 2 The Nonlinear Curvature
- 3 Local Lie Groups
- 4 The Centralizer
- 5 <i><span xml:lang="ell">ε</span></i>-Invariance
- 6 The Linear Curvature
- 7 The Structure Object
- Part II Some Consequences
- 8 The Nonlinear Spencer Sequence
- 9 Deformations
- 10 The de Rham Cohomology of an LLG
- 11 The Linear Spencer Sequence
- 12 The Secondary Characteristic Classes
- 13 The Homogeneous Flow
- 14 The Van Est Theorem
- 15 The Symmetry Group
- Part III How to Generalize?
- 16 Klein Geometries
- 17 The Universal Jet Groupoids
- 18 Embeddings of Klein Geometries into Universal Jet Groupoids
- 19 The Definition of a Prehomogeneous Geometry (PHG)
- 20 Curvature and Generalized PHGs
- Appendix Torsion-Free Connections
- References
- Index
