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Exponential actions, orbits and their kernels
Published online by Cambridge University Press: 17 April 2009
Abstract
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
*.
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- Research Article
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- Copyright © Australian Mathematical Society 1998
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