Élie Cartan

Élie Cartan , born the April 9th 1869 with Dolomieu and dead the May 6th 1951 with Paris, is one of the Mathématicien S French most influential of its time. Its work concerns the geometrical applications of the groups of Dregs.

Biography

Resulting from a modest milieu, Élie Joseph Cartan follows secondary studies to Grenoble and comes to Paris to the Lycée Janson-with-Sailly to prepare the admission with the National university. It is allowed there in 1888. It supports its doctorate in 1894, then sign successively in the universities of Montpellier, Lyon and Nancy. He becomes professor with the Sorbonne in 1912 and ensures a teaching the National university. He is professor of Géométrie and Mechanic with the University of industrial physics and chemistry of 1920 to 1940. He is elected member of the Academy of Science in 1931. He takes his retirement in 1942.

He is the father of the mathematician Henri Cartan.

The school of its native commune, Dolomieu, bears its name, as well as the college of sector located at Tour-du-Pin, under prefecture of Isere.

Work

Its first mathematical research relates to the groups and algebras of Dregs. One owes him in 1894 a classification of these last on the body of the complex numbers. It then turns to the theory of the associative algebras. About 1910, it introduces the concept of Spineur, complex Vecteur which makes it possible to express the Rotation S of the space by a two-dimensional representation and this, before the discovery of the Spin of the elementary particles in Quantum physics.

Since 1922, it contributes to refine certain mathematical tools of the General relativity (tensor of Ricci in particular), extending the geometry riemannienne of the general relativity, which will become geometry of Riemann-Cartan.

It introduced also the algebraic concept of Groupe, developed seriously only in second half of the twentieth century.

Theorist of talent, Élie Cartan has also a great aptitude to be rendered comprehensible with his students the most difficult concepts. Its work, very innovative, is recognized only tardily.

Élie Cartan classified the symmetrical spaces.

Works

  • Geometry of spaces of Riemann (1925)

  • the Theory of the continuous groups and generalized spaces (1935)
  • the Theory of the spinors (1938)

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