Drummond, T., Jotz Lean, M. and Ortiz, C. (2015) VB-algebroids morphisms and representations up to homotopy. Differential Geometry and its Applications, 40. pp. 332-357. ISSN 0926-2245
Abstract
We show in this paper that the correspondence between 2-term representations up to homotopy and VB-algebroids, established in [6], holds also at the level of morphisms. This correspondence is hence an equivalence of categories. As an application, we study foliations and distributions on a Lie algebroid, that are compatible both with the linear structure and the Lie algebroid structure. In particular, we show how infinitesimal ideal systems in a Lie algebroid A are related with subrepresentations of the adjoint representation of A.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Elsevier. This is an author produced version of a paper subsequently published in Differential Geometry and its Applications. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | VB-algebroids morphisms; Representations up to homotopy; Ideal systems |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Oct 2015 16:32 |
Last Modified: | 12 Apr 2017 19:45 |
Published Version: | https://doi.org/10.1016/j.difgeo.2015.03.005 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.difgeo.2015.03.005 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89087 |