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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Holomorphic string algebroids


Authors: Mario Garcia-Fernandez, Roberto Rubio and Carl Tipler
Journal: Trans. Amer. Math. Soc. 373 (2020), 7347-7382
MSC (2010): Primary 53D18; Secondary 32C38
DOI: https://doi.org/10.1090/tran/8149
Published electronically: July 29, 2020
MathSciNet review: 4155210
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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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Additional Information

Mario Garcia-Fernandez
Affiliation: Departamento Matemáticas, Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Cantoblanco, 28049 Madrid, Spain
MR Author ID: 921695
Email: mario.garcia@icmat.es

Roberto Rubio
Affiliation: Weizmann Institute of Science, 234 Herzl Street, Rehovot 76100, Israel
Address at time of publication: Universitat Autònoma de Barcelona, 08193 Barcelona, Spain
MR Author ID: 1032228
ORCID: 0000-0003-1645-1722
Email: roberto.rubio@uab.es

Carl Tipler
Affiliation: LMBA, UMR, CNRS 6205; Département de Mathématiques, Université de Bretagne Occidentale, 6, avenue Victor Le Gorgeu, 29238 Brest Cedex 3, France
MR Author ID: 1006281
Email: carl.tipler@univ-brest.fr

Received by editor(s): May 15, 2019
Received by editor(s) in revised form: March 10, 2020
Published electronically: July 29, 2020
Additional Notes: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 655162.
The first author was supported by Universidad Autónoma de Madrid and was initially supported by a Marie Sklodowska-Curie grant.
The second author was supported by the Weizmann Institute (ERC StG grant 637912, ISF grant 687/13) and was initially supported by IMPA
The third author was supported by the French government “Investissements d’Avenir” program ANR–11–LABX–0020–01 and ANR project EMARKS No. ANR–14–CE25–0010.
Article copyright: © Copyright 2020 American Mathematical Society