Examples of Groups: Lie Groups and Algebraic Groups

  • Igor R. Shafarevich
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 11)


We now turn to the consideration of groups whose elements are given by continuously varying parameters; in other words, these are groups, occuring frequently in connection with questions of geometry or physics, whose set of elements itself has a geometry. This geometry may sometimes be very simple, but at other times far from trivial.


Algebraic Group Quotient Group Compact Subgroup Orthogonal Transformation Maximal Compact Subgroup 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Igor R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of ScienceMoscowRussia

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