Symplectic structures on quadratic Lie algebras

By Ignacio Bajo, S. Benayadi, Alberto Medina. 2006

69 citations recorded by the source corpus.

Abstract We study quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure. We see that if K is algebraically closed every such Lie algebra may be constructed as the T ∗ -extension of a nilpotent Lie algebra admitting an invertible derivation and also as the double extension of another quadratic symplectic Lie algebra by the one-dimensional Lie algebra. Finally, we prove that every symplectic quadratic Lie algebra is a special symplectic Manin algebra and we give an inductive description in terms of symplectic quadratic double extensions.

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

View Paper: https://www.semanticscholar.org/paper/0bdbc4d4dfe9dc4b3a7d239d210cb6ee4c322b3f