Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie’s theory of finite continuous groups, critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan’s groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length.
The work concludes by discussing Cartan’s contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. About the Author - p. ix 6. Preface - p. xi 7. Acknowledgment - p. xvii 8. Chapter 1: Lie on the Backstage - p. xvii 9. Chapter 2: Cartan's Doctoral Dissertation - p. 12 10. Chapter 3: Infinite Continuous Groups 1883–1902 - p. 51 11. Chapter 4: Exterior Differential Systems - p. 107 12. Chapter 5: Cartan's Theory 1902–1909 - p. 150 13. Chapter 6: Cartan as a Geometer - p. 185 14. Appendix A: Picard–Vessiot Theory - p. 229 15. Appendix B: The Galois of His Generation - p. 239 16. Appendix C: Clifford's Parallelism - p. 249 17. Bibliography - p. 269 18. Index - p. 279
Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie’s theory of finite continuous groups, critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan’s groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length.
The work concludes by discussing Cartan’s contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. About the Author - p. ix 6. Preface - p. xi 7. Acknowledgment - p. xvii 8. Chapter 1: Lie on the Backstage - p. xvii 9. Chapter 2: Cartan's Doctoral Dissertation - p. 12 10. Chapter 3: Infinite Continuous Groups 1883–1902 - p. 51 11. Chapter 4: Exterior Differential Systems - p. 107 12. Chapter 5: Cartan's Theory 1902–1909 - p. 150 13. Chapter 6: Cartan as a Geometer - p. 185 14. Appendix A: Picard–Vessiot Theory - p. 229 15. Appendix B: The Galois of His Generation - p. 239 16. Appendix C: Clifford's Parallelism - p. 249 17. Bibliography - p. 269 18. Index - p. 279
