Symplectic or contact structures on Lie groups |
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Authors: | Yu. Khakimdjanov M. Goze |
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Affiliation: | a Université de Haute Alsace, 4, rue des Frères Lumière, 68093 Mulhouse Cedex, France b Université de Montpellier II, case 051, 34095 Montpellier Cedex 5, France |
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Abstract: | We study left invariant contact forms and left invariant symplectic forms on Lie groups. In the case of filiform Lie groups we give a necessary and sufficient condition for the existence of a left invariant contact form and we prove the uniqueness of this contact form up to a nonzero scalar multiple. As an application we classify all symplectic structures on nilpotent Lie algebras of dimension ?6. |
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Keywords: | 53Dxx 22E25 17B30 |
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