Holomorphic string algebroids

Garcia-Fernandez, Mario; Rubio, Roberto; Tipler, Carl

doi:10.1090/tran/8149

Holomorphic string algebroids
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by Mario Garcia-Fernandez, Roberto Rubio and Carl Tipler PDF

Trans. Amer. Math. Soc. 373 (2020), 7347-7382 Request permission

Abstract:

We introduce the category of holomorphic string algebroids, whose objects are Courant extensions of Atiyah Lie algebroids of holomorphic principal bundles and whose morphisms correspond to inner morphisms of the underlying holomorphic Courant algebroids. 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 Čech cohomology and the construction of a locally complete family of deformations of string algebroids via a differential graded Lie algebra.

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