Skip to main content
SpringerLink
Log in

On ergodic quasi-invariant measures of group automorphism

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We study the dynamics of projective transformations and apply it to (i) prove that the isotropy subgroups of probability measures on algebraic homogeneous spaces are algebraic and to (ii) study the class of ergodic quasi-invariant measures of automorphisms of non-compact Lie groups. It is shown that their support is always a proper subset and that under certain conditions on the Lie group the induced homeomorphism of the support is topologically equivalent to a translation of a compact group.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Borel,Linear Algebraic Groups, Benjamin, New York, 1969.

    MATH  Google Scholar 

  2. A. Borel,Introduction aux Groupes Arithmetiques, Publ. de l'inst. Math. de l'univ. de Strassbourg XV, Hermann, Paris, 1969.

    MATH  Google Scholar 

  3. C. Chevalley,Theory of Lie Groups, Princeton University Press, Princeton, 1946.

    MATH  Google Scholar 

  4. S. G. Dani,A simple proof of Borel's density theorem, Math. Z.174 (1980), 81–94.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Glimm,Locally compact transformation groups, Trans. Am. Math. Soc.101 (1961), 124–138.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Kaufman and M. Rajagopalan,On automorphisms of a locally compact group, Mich. Math. J.13 (1966), 373–374.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Montgomery and L. Zippin,Topological Transformation Groups, Interscience Publ., New York, 1955.

    MATH  Google Scholar 

  8. C. C. Moore,Ergodicity of flows on homogeneous spaces, Am. J. Math.88 (1966), 154–178.

    Article  MATH  Google Scholar 

  9. C. C. Moore,Amenable subgroups of semisimple groups and proximal flows. Isr. J. Math.34 (1979), 121–138.

    Article  MATH  Google Scholar 

  10. R. K. Thomas,On affine transformations of locally compact groups, J. Lond. Math. Soc.4 (1971), 599–610.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, 400 005, Bombay, India

    S. G. Dani

Authors
  1. S. G. Dani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dani, S.G. On ergodic quasi-invariant measures of group automorphism. Israel J. Math. 43, 62–74 (1982). https://doi.org/10.1007/BF02761685

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761685

Keywords

Search

Navigation