## 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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### References:

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