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On closed radical orbits in homogeneous complex manifolds

Published online by Cambridge University Press:  17 April 2009

Bruce Gilligan
Bruce Gilligan
Affiliation:
Department of Mathematics and Statistics, University of Regina Regina, Canada S4S 0A2, e-mail: gilligan@max.cc.uregina.ca
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Abstract

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Suppose G is a complex Lie group having a finite number of connected components and H is a closed complex subgroup of G with H° solvable. Let RG denote the radical of G. We show the existence of closed complex subgroups I and J of G containing H such that I/H is a connected solvmanifold with I° ⊃ RG, the space G/J has a Klein form SG/A, where A is an algebraic subgroup of the semisimple complex Lie group SG: = G/RG, and, unless I = J, the space J/I has Klein form , where is a Zariski dense discrete subgroup of some connected positive dimensional semisimple complex Lie group Ŝ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 363 - 368
Copyright
Copyright © Australian Mathematical Society 1996

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