论文标题
线性通用复合结构
Linear generalised complex structures
论文作者
论文摘要
本文研究了矢量束上的线性广义复合结构，这是全体形态矢量束的广义几何版本。在适应的线性分裂中，在向量捆绑包上的线性通用复杂结构$ e \ to m $等同于$ \ mathbb c $ -mmultiplication $ j $ in $ tm \ oplus e^*$ oplus e^*$和$ \ mathbb c $ -lie Algebroid结构的$ tm-lie Algebroid结构上的$ tm \ oplus e^*$。 然后在这种情况下研究了广义的复合物谎言代数（或Glanon代数），并表示为一对复杂的共轭躺椅。
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to M$ is equivalent to a $\mathbb C$-multiplication $j$ in the fibers of $TM\oplus E^*$ and $\mathbb C$-Lie algebroid structure on $TM\oplus E^*$. Generalised complex Lie algebroids (or Glanon algebroids) are then studied in this context, and expressed as a pair of complex conjugated Lie bialgebroids.
