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arXiv 2011.146522020-11math.DG

Linear generalised complex structures

Malte Heuer, Madeleine Jotz Lean

备注：: 36 pages

英文摘要：

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.

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