1988
DOI: 10.1007/bf00398959
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On Lie groups with left-invariant symplectic or K�hlerian structures

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Cited by 89 publications
(93 citation statements)
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“… Geometry of Erich Kähler: Study of differential manifolds geometry equipped with a unitary structure satisfying a condition of integrability. The homogeneous Kähler case studied by André André Lichnerowicz [110].…”
Section: Conclusion and Possible Extensionsmentioning
confidence: 99%
“… Geometry of Erich Kähler: Study of differential manifolds geometry equipped with a unitary structure satisfying a condition of integrability. The homogeneous Kähler case studied by André André Lichnerowicz [110].…”
Section: Conclusion and Possible Extensionsmentioning
confidence: 99%
“…ii) A complete description of symplectic Lie algebras of dimension 4 was obtained in [27] (for a detailed study of symplectic Lie algebras, see also [5,21]). Thus, one can determine all contact Lie algebras of dimension 5 with center of dimension 1 and from there, using Theorem 4.1, to obtain different examples of generalized Lie bialgebras.…”
Section: -Let (H [ ]mentioning
confidence: 99%
“…They were first mentioned by Cayley in 1890 [20] as a kind of rooted tree algebra and later arose again from the study of convex homogeneous cones [53], affine manifold and affine structures on Lie groups [40], and deformation of associative algebras [34]. They play an important role in the study of symplectic and complex structures on Lie groups and Lie algebras [5,22,24,25,44], phases spaces of Lie algebras [8,42], certain integrable systems [16], classical and quantum Yang-Baxter equations [26], combinatorics [27], quantum field theory [23] and operads [19]. See [17] for a survey.…”
Section: Introductionmentioning
confidence: 99%