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Characteristically nilpotent Lie algebras and symplectic structures. (English) Zbl 1206.17009

Summary: We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space \(H^2({\mathfrak g} ,k)\) for certain Lie algebras \(\mathfrak g\). Among these Lie algebras are filiform CNLAs of dimension \(n\geq 14\). It turns out that there are many examples of CNLAs which admit a symplectic structure. A generalization of a symplectic structure is an affine structure on a Lie algebra.

MSC:

17B30 Solvable, nilpotent (super)algebras
53D05 Symplectic manifolds (general theory)
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