Lie Groups

Jacques Lafontaine
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Jacques Lafontaine: Université Montpellier 2, Département de Mathématiques

Chapter Chapter 4 in An Introduction to Differential Manifolds, 2015, pp 147-183 from Springer

Abstract: Abstract The notion of group was singled out around 1830 by Évariste Galois in his work on algebraic equations. This initial work was with finite groups. Forty years later, the work of Galois inspired the Norwegian mathematician Sophus Lie, who rather than studying invariance of algebraic equations was studying the invariance properties of ordinary and partial differential equations and put the need for other types of groups into focus. These were formerly called “finite and continuous groups”, which in today’s language conveys groups of finite topological dimension. In fact many of the examples discovered were smooth manifolds, with smooth group operations. Today we call such groups Lie groups.

Keywords: Universal Covering; Discrete Subgroup; Left Translation; Left Invariant Vector Field; Pure Quaternion (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-20735-3_4

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