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Writing Small Omegas

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

1st Edition - October 24, 2017

Author: Alberto Cogliati

Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 1 4 2 4 4 - 8
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 1 4 2 7 4 - 5

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, criticall… Read more

Writing Small Omegas

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critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters.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