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Transactions of the American Mathematical Society

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



Symplectic homogeneous spaces

Author: Shlomo Sternberg
Journal: Trans. Amer. Math. Soc. 212 (1975), 113-130
MSC: Primary 22E45; Secondary 58F05
MathSciNet review: 0379759
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Abstract: In this paper we make various remarks, mostly of a computational nature, concerning a symplectic manifold X on which a Lie group G acts as a transitive group of symplectic automorphisms. The study of such manifolds was initiated by Kostant [4] and Souriau [5] and was recently developed from a more general point of view by Chu [2].

The first part of this paper is devoted to reviewing the Kostant, Souriau, Chu results and deriving from them a generalization of the Cartan conjugacy theorem. In the second part of this paper we apply these results to Lie algebras admitting a generalized (k, p) decomposition.

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Article copyright: © Copyright 1975 American Mathematical Society