Symplectic structures on quadratic Lie algebras
Symplectic structures on quadratic Lie algebras
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DOI：
10.1016/j.jalgebra.2007.06.001
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发表时间：
2006-03
影响因子：
0.9
通讯作者：
I. Bajo;S. Benayadi;Alberto Medina
中科院分区：
文献类型：
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作者：
I. Bajo;S. Benayadi;Alberto Medina
研究了零特征域K上的同时具有辛结构的二次李代数。我们看到，如果K是代数闭的，每个这样的李代数都可以被构造为一个允许可逆导数的幂零李代数的T-∗-扩张，也可以被构造为另一个二次辛李代数在一维李代数上的双重扩张。最后，我们证明了每个辛二次李代数都是一个特殊的辛Manin代数，并用辛二次双扩张给出了一个归纳刻画。
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.