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Homogeneous Spaces of Nilpotent and Solvable Groups

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

Abstract

Homogeneous spaces of nilpotent and solvable Lie groups are called nilmanifolds and solvmanifolds respectively. In addition it is assumed that the transitive Lie group is connected. At this time no comprehensive classification of nil- and solvmanifolds is known, as there is no classification of nilpotent and solvable Lie algebras. In this chapter we give a survey of results, which reduce the study of arbitrary nil- and solvmanifolds to the compact case, and also of results about topological construction of compact nil- and solvmanifolds and about transitive actions of Lie groups on them.

Keywords

  • Vector Bundle
  • Fundamental Group
  • Homogeneous Space
  • Klein Bottle
  • Transitive Action

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). Homogeneous Spaces of Nilpotent and Solvable Groups. 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_10

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  • DOI: https://doi.org/10.1007/978-3-642-57999-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61222-3

  • Online ISBN: 978-3-642-57999-8

  • eBook Packages: Springer Book Archive