Academic Press Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 (Studies in the History of Mathematical Inquiry)

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critically examining Cartan's doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters.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. Review "This is necessarily a very heavily mathematical book, which nevertheless manages to balance the need for such detail with an awareness of the historical context - great effort appears to have been taken, for example, to ensure that Cartan’s mathematics is interpreted on his terms, rather than in a modern way. The referencing throughout is sufficiently detailed to enable the reader to follow up on any points of interest, and a comprehensive index makes the book easy to navigate. This is an extremely valuable contribution to the study of the history of modern mathematics." --Zentralblatt Math Review Presents Élie Cartan’s seminal contributions to the theory of continuous groups, including the origins of his celebrated method of moving frames From the Back Cover 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 Lies theory of finite continuous groups, the work critically examines Cartans doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters.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, Cartans 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 Cartans 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 groups Reviews Cartans revolutionary contributions to Lie group theory and differential geometry Evaluates many unpublished sources shedding light on important aspects of the historical development of lie algebras About the Author 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 Cartans 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. About the Series Series Editor: Umberto Bottazzini EAB: Christian Gilain, Niccolo Guicciardini, Alexander Jones, Han Qi, David Rowe, Tilman Sauer This series consists of germane historical, historiographical, sociological, epistemological, geographical, and biographical treatments pertaining to the development and expansion of mathematics and prominent mathematicians. Volumes provide informed studies on mathematicians and their work in historical context, on historiographical topics in the history of mathematics, and on the interrelationships between m