Poincaré and the idea of a group

Titre :

Poincaré and the idea of a group

Sujet :

Mathématiques

Description :

In many different fields of mathematics and Physics Poincar´e found many uses for the idea of||a group, but not for group theory. He used the idea in his work on automorphic functions, in number theory, in his epistemology, Lie theory (on the so-called Campbell–Baker–Hausdorff and Poincar´e–Birkhoff–Witt theorems), in physics (where he introduced the Lorentz group), in his study of the domains of complex functions of several variables, and in his pioneering study of 3-manifolds. However, as a general rule, he seldom appealed to deep results in group theory, and developed no more structural analysis of any group than was necessary to solve a problem. It was usually enough for him that there is a group, or that there are different groups.||In this article Jeremy Gray gives a brief history on Poincar´e’s group idea.

Créateur :

Gray, Jeremy

Date :

2012-09

Droits :

Nieuw Archief voor Wiskunde

Format :

application/pdf

Langue :

en

Type :

Article de revue ; Texte

Description

In many different fields of mathematics and Physics Poincar´e found many uses for the idea of||a group, but not for group theory. He used the idea in his work on automorphic functions, in number theory, in his epistemology, Lie theory (on the so-called Campbell–Baker–Hausdorff and Poincar´e–Birkhoff–Witt theorems), in physics (where he introduced the Lorentz group), in his study of the domains of complex functions of several variables, and in his pioneering study of 3-manifolds. However, as a general rule, he seldom appealed to deep results in group theory, and developed no more structural analysis of any group than was necessary to solve a problem. It was usually enough for him that there is a group, or that there are different groups.||In this article Jeremy Gray gives a brief history on Poincar´e’s group idea.

Auteur

Gray, Jeremy

Date

2012-09

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