Death:1951May 6th in Paris.

Nationality: France

Details: Elie Joseph Cartan is a famous French mathematician. His main contributions are Lie groups, differential equations and geometry. His contribution has an important influence on the development of modern mathematics.

In the early days, he continued the work of killing people by Li and German mathematicians. 1894, he published the Construction of Finite Dimensional Continuous Transformation Groups, in which Keeling's theory of continuous transformation groups was revised and the complete classification of simple Lie algebras in complex fields was strictly proved. 19 13 completed the finite representation theory of semi-simple lie algebras, which laid the foundation for the representation theory of lie groups. When solving the representation of simple Lie algebras, he discovered the spinor (which has important applications in quantum mechanics and elementary particle theory) and proposed the rotation representation of orthogonal group Lie algebras.

The second aspect of his research on Lie groups is to discuss the global properties of Lie groups, that is, their topological properties. He used a very original method to calculate the Betty number of Lie groups, and asserted that the dimension of the homology group of Belgian mathematician De Ram was Betty number (this assertion was later proved by De Ram). He replaced the differential formula with the left invariant differential formula, which turned the calculation of Betty number into a pure arithmetic problem and finally solved it.

In terms of partial differential equations, he developed pfaff's equation theory and showed a strong geometric tendency in his method. His theory of partial differential equations made him make outstanding achievements in infinite lie groups, differential geometry, analytical mechanics and general relativity. After 1920, under the influence of the development of relativity, Jiadang has done a series of work in differential geometry. He developed the method of moving frames on general manifolds, established the geometry of affine connections, projective connections and conformal connections, discovered and studied symmetric Riemannian spaces, and made a deep study of connections. The generalized space he proposed is the predecessor of the concept of fiber bundle and the unity of Klein geometry and Riemann geometry. In "Theory and Position Analysis of Finite Continuous Groups" published by 1930, he summarized the previous studies and proved a series of new theorems, including manifold, continuous group, Lie group, homogeneous space and other clearer concepts, proved that the closed subgroup of a Lie group is a Lie group, proved the inverse theorem of Lie's third basic theorem for the first time, and proved the topological product of a simply connected Lie group with a maximal compact subgroup and Euclidean space.

He freely developed the method of moving coordinate system founded by Dabu, and made numerous contributions to Lee Group Theory, pfaff formalism, invariant integral theory, phase science, differential geometry (especially connected geometry), theoretical physics and so on. His paper still attracts the attention of many young researchers, and the concept of connectivity he created has become a basic concept in differential geometry. In his later years, Jia Dang developed the theory of symmetric space and put forward the theory of quasi-conformal mapping.