Nonconnected Lie Groups

  • Joachim HilgertEmail author
  • Karl-Hermann Neeb
Part of the Springer Monographs in Mathematics book series (SMM)


The examples from Chapter  17 show that many geometrically defined Lie groups have several connected components. While only the connected component of the identity is accessible to the methods built on the exponential function, there are still tools to analyze nonconnected Lie groups. In the present chapter, we present some of these tools. The key notion is that of an extension of a discrete group by a (connected) Lie group.


  1. [Bl73]
    Blattner, R. J., Quantization and representation theory, in “Harmonic analysis on homogeneous spaces” (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), pp. 147–165, Amer. Math. Soc., Providence, RI, 1973 Google Scholar
  2. [ML63]
    MacLane, S., “Homological Algebra, ” Springer-Verlag, Berlin, 1963 Google Scholar
  3. [Ne07]
    Neeb, K.-H., Nonabelian extensions of infinite-dimensional Lie groups, Ann. Inst. Fourier 56 (2007), 209–271 MathSciNetCrossRefGoogle Scholar
  4. [We95]
    Weibel, C. A., “An Introduction to Homological Algebra”, Cambridge Studies in Advanced Math. 38, Cambridge Univ. Press, Cambridge, 1995 zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of PaderbornPaderbornGermany
  2. 2.Department of MathematicsFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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