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Exponential actions, orbits and their kernels

Published online by Cambridge University Press:  17 April 2009

J. Ludwig  and
C. Molitor-Braun
J. Ludwig
Affiliation:
Département de MathématiquesUniversité de Metz, Ile de SaulcyF-57045 Metz cedex 1France
C. Molitor-Braun
Affiliation:
Séminaire de MathématiqueCentre Universitaire de Luxembourg, 162A Avenue de la FaïencerieL-1511 LuxembourgLuxembourg
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Abstract

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Let be a nilpotent Lie algebra which is an exponential -module, being an exponential algebra of derivations of . Put = exp and = exp . If Ω is a closed orbit of * under the action of , then Ker is dense in Ker Ω for the topology of L1 () and the algebra Ker is nilpotent, where denotes the minimal closed ideal of L1() whose hull is Ω. Moreover, the -prime ideals of Ll() coincide with the kernels Ker Ω, where Ω denotes an arbitrary orbit (not necessarily closed) in *.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 497 - 513
Copyright
Copyright © Australian Mathematical Society 1998

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