论文标题
左不变特殊Kähler结构
Left invariant special Kähler structures
论文作者
论文摘要
我们在一个平坦的伪里曼式谎言组的cotangent捆绑包上构建了不变的特殊kähler结构。我们根据InfitInitesimalKähler变换的两种线性表示，介绍了两个特殊的KählerLie代数的扭曲笛卡尔产品。我们还展示了特殊的KählerLie代数的双重扩展过程，该过程使我们能够通过双重不变的符号连接使所有简单地连接的特殊KählerLie组。通过执行此双重扩展过程构建的所有谎言组都可以通过其Lie代数的符号（或Kähler）仿射转换的亚组识别，该子代数包含由中央翻译形成的非平凡$ 1 $参数亚组。我们展示了使用étaleKähler仿射表示的左扁平特殊kähler结构的表征，表现出上述结构的一些直接后果，并给出了几个非平凡的例子。
We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial $1$-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.
