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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Orbits in a real reductive Lie algebra


Author: L. Preiss Rothschild
Journal: Trans. Amer. Math. Soc. 168 (1972), 403-421
MSC: Primary 17B20; Secondary 57E25
DOI: https://doi.org/10.1090/S0002-9947-1972-0349778-3
MathSciNet review: 0349778
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Abstract: The purpose of this paper is to give a classification of the orbits in a real reductive Lie algebra under the adjoint action of a corresponding connected Lie group. The classification is obtained by examining the intersection of the Lie algebra with the orbits in its complexification. An algebraic characterization of the minimal points in the closed orbits is also given.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0349778-3
Keywords: Real Lie algebra, reductive algebraic group, conjugacy classes, real Lie groups, homogeneous spaces of Lie groups
Article copyright: © Copyright 1972 American Mathematical Society

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