Writing Small Omegas

Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926

Alberto Cogliati (Autor)

Buch | Softcover

304 Seiten

2017
Academic Press Inc (Verlag)
978-0-12-814244-8 (ISBN)

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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critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters.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.

Alberto Cogliati, currently Assistant Professor at the Department of Mathematics ‘F. Enriques’ of the Università degli Studi di Milano. He received his PhD in March 2012 discussing Cartan’s structural approach to the theory of continuous groups of transformations. His main research interest is the history of 19th-20th mathematics, especially differential geometry, the history of Lie groups and the theory of connections.

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

Erscheinungsdatum	06.11.2017
Reihe/Serie	Studies in the History of Mathematical Inquiry
Verlagsort	San Diego
Sprache	englisch
Maße	152 x 229 mm
Gewicht	450 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	0-12-814244-8 / 0128142448
ISBN-13	978-0-12-814244-8 / 9780128142448
Zustand	Neuware