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Let $mathfrak{sp}_{2n}(mathbb {K})$ be the symplectic Lie algebra over an algebraically closed field of characteristic zero. We prove that for any nonzero nilpotent element $X in mathfrak{sp}_{2n}(mathbb {K})$ there exists a nilpotent element $Y in mathfrak{sp}_{2n}(mathbb {K})$ such that $X$ and $Y$ generate $mathfrak{sp}_{2n}(mathbb {K})$.
Consider the special linear Lie algebra $mathfrak{sl}_n(mathbb {K})$ over an infinite field of characteristic different from $2$. We prove that for any nonzero nilpotent $X$ there exists a nilpotent $Y$ such that the matrices $X$ and $Y$ generate the Lie algebra $mathfrak{sl}_n(mathbb {K})$.
We study symplectic structures on nilpotent Lie algebras. Since the classification of nilpotent Lie algebras in any dimension seems to be a crazy dream, we approach this study in case of 2-step nilpotent Lie algebras (in this sub-case also, the class
We describe some examples of non abelian nilpotent Lie algebras which are not algebraic.
The classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given Lie algebra
In this paper, we study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an algebraically closed field of characteristic zero. As an application, we p