Symplectic or contact structures on Lie groups

By Y. Khakimdjanov, Michel Goze, A. Medina. 2002

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c0b01eb3ee78c8e7e08cf4f9876d2e772739b86