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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 7347-7382
  • MSC (2010): Primary 53D18; Secondary 32C38
  • DOI: https://doi.org/10.1090/tran/8149
  • MathSciNet review: 4155210