Writing small omegas : Élie Cartan's contributions to the theory of continuous groups, 1894-1926
Author(s)
Bibliographic Information
Writing small omegas : Élie Cartan's contributions to the theory of continuous groups, 1894-1926
（Studies in the history of mathematical enquiry / series editor, Umberto Bottazzini）
Academic Press, c2018
- : [pbk.]
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Note
Includes bibliographical references (p. 269-277) and index
Description and Table of Contents
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critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters.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.
Table 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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