On the dual of an exponential solvable Lie group
Author:
Bradley N. Currey
Journal:
Trans. Amer. Math. Soc. 309 (1988), 295-307
MSC:
Primary 22E27
DOI:
https://doi.org/10.1090/S0002-9947-1988-0957072-4
MathSciNet review:
957072
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a connected, simply connected exponential solvable Lie group with Lie algebra
. The Kirillov mapping
gives a natural parametrization of
by co-adjoint orbits and is known to be continuous. In this paper a finite partition of
is defined by means of an explicit construction which gives the partition a natural total ordering, such that the minimal element is open and dense. Given
, elements in the enveloping algebra of
are constructed whose images under
are scalar and give crucial information about the associated orbit. This information is then used to show that the restriction of
to each element of the above-mentioned partition is a homeomorphism.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1988-0957072-4
Article copyright:
© Copyright 1988
American Mathematical Society