论文标题
复杂的符号谎言代数和大的阿贝利亚子代数
Complex Symplectic Lie Algebras with Large Abelian Subalgebras
论文作者
论文摘要
我们介绍了具有大的阿贝尔理想的代数上的复杂符号结构的两个结构。特别是，我们完全对几乎阿贝利亚的代数分类进行了复杂的同骨结构。通过考虑其相应连接的紧凑型商，简单地连接的谎言组，我们获得了许多不带（超级）kähler指标的复杂符号歧管的例子。我们还产生了紧凑的复杂符号歧管的示例，并具有纤维是拉格朗日摩ri的纤维。
We present two constructions of complex symplectic structures on Lie algebras with large abelian ideals. In particular, we completely classify complex symplectic structures on almost abelian Lie algebras. By considering compact quotients of their corresponding connected, simply connected Lie groups we obtain many examples of complex symplectic manifolds which do not carry (hyper)kähler metrics. We also produce examples of compact complex symplectic manifolds endowed with a fibration whose fibers are Lagrangian tori.
