Writing Small Omegas: Elie Cartans Contributions to the Theory of Continuous Groups 1894-1926

Writing Small Omegas provides a historical analysis of Elie Cartan's seminal contributions to the theory of continuous groups (both finite and infinite) between 1893 and 1926. Opening with a general account of Lie's theory of finite continuous groups, the work critically examines Cartan's doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters.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. Discusses the origins of the theory of moving frames and the geometrical theory of Lie groupsReviews Cartan's revolutionary contributions to Lie group theory and differential geometryEvaluates many unpublished sources shedding light on important aspects of the historical development of lie algebras INDICE: 1. Lie on the backstage 2. Cartan's doctoral dissertation 3. Infinite Continuous Groups 1883-1902 4. Exterior Differential Systems 5. Cartan's Theory (1902-1909) 6. The method of moving frames 7. The geometry of continuous groups 8. Conclusion

• ISBN: 978-0-12-814244-8
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 300
• Fecha Publicación: 01/11/2017
• Nº Volúmenes: 1
• Idioma: Inglés