Writing Small Omegas
Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926
Series: Studies in the History of Mathematical Inquiry;
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Product details:
- Publisher Elsevier Science
- Date of Publication 24 October 2017
- ISBN 9780128142448
- Binding Paperback
- No. of pages304 pages
- Size 228x152 mm
- Weight 450 g
- Language English 0
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Long description:
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critically examining Cartan's doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters.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.
MoreTable of Contents:
1. Lie on the backstage2. Cartan's doctoral dissertation3. Infinite Continuous Groups 1883-19024. Exterior Differential Systems5. Cartan's Theory (1902-1909)6. The method of moving frames7. The geometry of continuous groups8. Conclusion
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