Skip to main content
SpringerLink
Log in

Etale Affine Representations of Lie Groups

  • Chapter
Geometry and Representation Theory of Real and p-adic groups

Part of the book series: Progress in Mathematics ((PM,volume 158))

Abstract

Let G be a finite-dimensional connected Lie group with Lie algebra g. Denote by E a real vector space and by Aff(E) the group of affine automorphisms

$${\text{Aff}}\left( E \right) = \left\{ {\left( {\begin{array}{*{20}{c}} A&b \\ 0&1 \end{array}} \right)|A \in {\text{GL}}\left( E \right),{\text{ }}b \in E} \right\}$$

.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Abels, G.A. Margulis and G.A. Soifer, On the Zariski closure of the linear part of a properly discontinuous group of affine transformations, Preprint (1995).

    Google Scholar 

  2. L. Auslander, Simply transitive groups of affine motions, Amer. J. Math. 99 (1977), 809–826.

    Article  MathSciNet  MATH  Google Scholar 

  3. O. Baues, Flache Strukturen auf GL(n) und zugehörige linkssymmetrische Algebren, Dissertation, Düsseldorf 1995.

    Google Scholar 

  4. Y. Benoist, Une nilvariété non affine, J. Diff. Geometry 41 (1995), 21–52.

    MathSciNet  MATH  Google Scholar 

  5. D. Burde and F. Grunewald, Modules for certain Lie algebras of maximal class, J. of pure and appi Algebra, 99 (1995), 239–254.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Burde, Left-symmetric structures on simple modular Lie algebras, J. Algebra 169 (1994), 112–138.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Burde, Left-invariant affine structures on reductive Lie groups, J. of Algebra 181 (1996), 884–902.

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Burde, Affine structures on nilmanifolds, International Journal of Math. 7: 5 (1996), 599–616.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Burde, On a Refinement of Ado’s Theorem, to appear in Archiv der Mathematik.

    Google Scholar 

  10. D. Fried, W. Goldman and M.W. Hirsch, Affine manifolds with nilpotent holonomy, Comment. Math. Helv. 56 (1981), 487–523.

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. B. Hakimjanov, Variété des lois d’àlgèbres de Lie nilpotentes Geometriae Dedicata 40 (1991), 269–295.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Helmstetter, Algèbres symétriques à gauche, C.R. Acad. Se. Paris 272 (1971), 1088–1091.

    MathSciNet  MATH  Google Scholar 

  13. J. Jantzen, First cohomology groups for classical Lie algebras, Prog. Math. 95 (1991), 289–315.

    MathSciNet  Google Scholar 

  14. H. Kim, Complete left-invariant affine structures on nilpotent Lie groups, J. Differential Geometry 24 (1986), 373–394.

    MATH  Google Scholar 

  15. J. Milnor, On fundamental groups of complete affinely flat manifolds, Advances in Math. 25 (1977), 178–187.

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Segal, The structure of complete left-symmetric algebras, Math. Ann. 293 (1992), 569–578.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Smillie, An obstruction to the existence of affine structures, Inventions Math. 64 (1981), 411–415.

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Vergne, Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes, Bull. Math. Soc. France 78 (1970), 81–116.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Heinrich-Heine Universität Dusseldorf, D-40225, Dusseldorf, Germany

    Dietrich Burde

Authors
  1. Dietrich Burde
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Facultad de Mathemática, Astronomia y Fisica, Universidad Nacional de Córdoba Ciudad Universitaria, 5000, Córdoba, Argentina

    Juan Tirao

  2. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    David A. Vogan Jr.

  3. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Joseph A. Wolf

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Birkhäuser Boston

About this chapter

Cite this chapter

Burde, D. (1998). Etale Affine Representations of Lie Groups. In: Tirao, J., Vogan, D.A., Wolf, J.A. (eds) Geometry and Representation Theory of Real and p-adic groups. Progress in Mathematics, vol 158. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4162-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4162-1_3

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8681-3

  • Online ISBN: 978-1-4612-4162-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation