On Ergodic quasi-invariant measures of group automorphism

Dani, S. G. (1992) On Ergodic quasi-invariant measures of group automorphism Israel Journal of Mathematics, 43 (1). pp. 62-74. ISSN 0021-2172

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Official URL: http://www.springerlink.com/content/1443510mu85664...

Related URL: http://dx.doi.org/10.1007/BF02761685


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.

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