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Introduction

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Part of the Encyclopaedia of Mathematical Sciences book series (EMS,volume 20)

Abstract

The theory of Lie groups, to which this volume is devoted, is one of the classical well established chapters of mathematics. There is a whole series of monographs devoted to it (see, for example, Pontryagin 1984, Postnikov 1982, Bourbaki 1947, Chevalley 1946, Helgason 1962, Sagle and Walde 1973, Serre 1965, Warner 1983). This theory made its first appearance at the end of the last century in the works of S. Lie, whose aim was to apply algebraic methods to the theory of differential equations and to geometry. During the past one hundred years the concepts and methods of the theory of Lie groups entered into many areas of mathematics and theoretical physics and became inseparable from them.

Keywords

  • Theoretical Physic
  • Tangent Space
  • Topological Group
  • Associative Algebra
  • Cell Complex

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1993 Springer-Verlag Berlin Heidelberg

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Onishchik, A.L. (1993). Introduction. In: Onishchik, A.L. (eds) Lie Groups and Lie Algebras I. Encyclopaedia of Mathematical Sciences, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57999-8_1

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  • DOI: https://doi.org/10.1007/978-3-642-57999-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61222-3

  • Online ISBN: 978-3-642-57999-8

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