Jotz Lean, M. and Ortiz, C. (2014) Foliated groupoids and infinitesimal ideal systems. Indagationes Mathematicae, 25 (5). pp. 1019-1053. ISSN 0019-3577
Abstract
The main goal of this work is to introduce a natural notion of ideal in a Lie algebroid, the “infinitesimal ideal systems”. Ideals in Lie algebras and the Bott connection associated to involutive subbundles of tangent bundles are special cases. The definition of these objects is motivated by the infinitesimal description of involutive multiplicative distributions on Lie groupoids. In the Lie group case, such distributions correspond to ideals. Several examples of infinitesimal ideal systems are presented, and (under suitable regularity conditions) the quotient of a Lie algebroid by an infinitesimal ideal system is shown to be a Lie algebroid.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 Elsevier. This is an author produced version of a paper subsequently published in Indagationes Mathematicae. 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: | Lie algebroids and Lie groupoids; Multiplicative geometric structures; Ideals; Linear connections; Bott connection |
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 16:25 |
Last Modified: | 16 Nov 2016 09:21 |
Published Version: | https://doi.org/10.1016/j.indag.2014.07.009 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.indag.2014.07.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89089 |