Claude Chevalley

Claude Chevalley was a French mathematician. He was born on February 11, 1909, and died on June 28, 1984.

He made important contributions to many areas of mathematics. These areas include number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups.

Chevalley was one of the founding members of the Bourbaki group. This was a group of mathematicians who worked together to build a new foundation for modern mathematics. His work helped shape how mathematicians understand numbers and structures today.

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Life

Claude Chevalley was a French mathematician. He lived from 1909 to 1984. His father helped write a well-known French dictionary. Chevalley studied in France and Germany, learning 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 taught at Columbia University. He became an American citizen and wrote many important math papers in English. Later, he returned to France and taught at the University of Paris. Chevalley was also interested in art and politics and joined some creative groups in the 1930s.

Work

Claude Chevalley did important work in math, especially in number theory and algebraic geometry.

In his PhD, he helped develop class field theory by using a new algebraic method.

In the 1950s, Chevalley wrote books about Lie groups and discovered what we now call Chevalley groups. These groups are important in the study of finite simple groups. He also helped us understand Lie algebras better and made it possible to study these groups over finite fields. His ideas are still used today in solving equations and studying shapes in algebraic geometry.

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

Recognition

In 2014, the American Mathematical Society made the Chevalley Prize in Lie Theory to honor big work in this part of math. The first person to get this prize was Geordie Williamson in 2016. After that, more people got the prize for their work, like 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.