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Generalizations of Lie Groups

  • A. L. Onishchik
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 20)

Abstract

This chapter contains a brief survey of certain theories generalizing the classical Lie theory. This survey does not aspire to completeness. In particular, we do not touch on the theory of algebraic groups and topological groups are considered only in connection with Hilbert’s 5th problem. These subjects, naturally, require separate surveys. The same can be said about “infinite” continuous groups (or Lie pseudo-groups), the study of which was originated already by S. Lie. Beyond the scope of this survey remain the Kac-Moody algebras and the groups corresponding to them, as well as Lie supergroups and superalgebras.

Keywords

Moufang Loop Frechet Space Geodesic Loop Tangent Algebra Local Analytic Loop 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • A. L. Onishchik
    • 1
  1. 1.Yaroslavl UniversityYaroslavlRussia

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