Claude Chevalley

Claude Chevalley was a French mathematician born on February 11, 1909, and passed away on June 28, 1984. He made important contributions to several areas of mathematics, including number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups.

Chevalley was also one of the founding members of the Bourbaki group, a collection of mathematicians who worked together to create a new foundation for modern mathematics. His work helped shape how mathematicians understand numbers and structures today. For information about another person named Claude Chevalley who played basketball for Switzerland in the Olympics, you can visit this page: Claude Chevalley (basketball).

Life

Claude Chevalley was a French mathematician who lived from 1909 to 1984. His father was a diplomat who helped write a well-known French dictionary. Chevalley studied at a special school in France and later in Germany, where he learned about Japanese mathematics. He earned his highest degree in 1933 with a study about number theory.

When World War II started, Chevalley was in the United States at Princeton University. He stayed there and later taught at Columbia University. He became an American citizen and wrote many important math papers in English. Eventually, he returned to France and taught at the University of Paris. Besides math, Chevalley was also interested in art and politics and was part of some creative groups in the 1930s.

Work

Claude Chevalley did important work in math, especially in areas like number theory and algebraic geometry. In his PhD, he helped develop a part of math called class field theory by using a new algebraic method instead of something called L-functions.

In the 1950s, Chevalley wrote books about Lie groups and discovered what we now call Chevalley groups. These groups are important examples in the study of finite simple groups. He also made key contributions to understanding Lie algebras and helped make it possible to study these groups over finite fields. His theorems are still used today in areas like solving equations over finite fields and studying shapes in algebraic geometry.

Chevalley also led important math seminars in Paris during the 1950s, which covered topics like algebraic groups and the foundations of algebraic geometry. These seminars helped shape the development of modern math.

Recognition

In 2014, the American Mathematical Society created the Chevalley Prize in Lie Theory to honor important work in this area of math. The first person to receive this prize was Geordie Williamson in 2016. Since then, others have been recognized for their contributions, including Dennis Gaitsgory, Huanchen Bao, Weiqiang Wang, Xuhua He, Victor Ostrik, Tasho Kaletha, and Zhiwei Yun.

Selected bibliography

Claude Chevalley wrote many important books and papers about math. Some of his well-known works include:

• 1936. L'Arithmetique dans les Algèbres de Matrices. Hermann, Paris.
• 1940. "La théorie du corps de classes," Annals of Mathematics 41: 394–418.
• 1946. Theory of Lie groups. Princeton University Press.
• 1951. "Théorie des groupes de Lie, tome II, Groupes algébriques", Hermann, Paris.
• 1951. Introduction to the theory of algebraic functions of one variable, A.M.S. Math. Surveys VI.
• 1954. The algebraic theory of spinors, Columbia Univ. Press; new edition, Springer-Verlag, 1997.
• 1953–1954. Class field theory, Nagoya University.
• 1955. "Théorie des groupes de Lie, tome III, Théorèmes généraux sur les algèbres de Lie", Hermann, Paris.
• 1955. "Sur certains groupes simples," Tôhoku Mathematical Journal 7: 14–66.
• 1955. The construction and study of certain important algebras, Publ. Math. Soc. Japan.
• 1956. Fundamental concepts of algebra, Acad. Press.
• 1956–1958. "Classification des groupes de Lie algébriques", Séminaire Chevalley, Secrétariat Math., 11 rue P. Curie, Paris; revised edition by P.Cartier, Springer-Verlag, 2005.
• 1958. Fondements de la géométrie algébrique, Secrétariat Math., 11 rue P. Curie, Paris.