We introduce the category of holomorphic string algebroids, whose objects are Courant extensions of Atiyah Lie algebroids of holomorphic principal bundles, as considered by Bressler, and whose morphisms correspond to inner morphisms of the underlying holomorphic Courant algebroids in the sense of Severa. This category provides natural candidates for Atiyah Lie algebroids of holomorphic principal bundles for the (complexified) string group and their morphisms. Our main results are a classification of string algebroids in terms of Cech cohomology, and the construction of a locally complete family of deformations of string algebroids via a differential graded Lie algebra.

中文翻译：

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全纯弦代数

我们介绍了全纯弦代数体的范畴，其对象是 Bressler 所考虑的全纯主丛的 Atiyah Lie 代数体的 Courant 扩展，其态射对应于 Severa 意义上的底层全纯 Courant 代数体的内态射。该类别为（复）弦群及其态射的全纯主丛的 Atiyah Lie 代数体提供了自然候选。我们的主要结果是根据切赫上同调对弦代数进行分类，以及通过微分分级李代数构建弦代数变形的局部完整族。