Cartan Connections on Lie Groupoids and their Integrability
A multiplicatively closed, horizontal n-plane field D on a Lie groupoid G over M generalizes to intransitive geometry the classical notion of a Cartan connection. The infinitesimalization of the connection D is a Cartan connection ∇ on the Lie algebroid of G, a notion already studied elsewhere by th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148549 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Cartan Connections on Lie Groupoids and their Integrability / A.D. Blaom // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | A multiplicatively closed, horizontal n-plane field D on a Lie groupoid G over M generalizes to intransitive geometry the classical notion of a Cartan connection. The infinitesimalization of the connection D is a Cartan connection ∇ on the Lie algebroid of G, a notion already studied elsewhere by the author. It is shown that ∇ may be regarded as infinitesimal parallel translation in the groupoid G along D. From this follows a proof that D defines a pseudoaction generating a pseudogroup of transformations on M precisely when the curvature of ∇ vanishes. A byproduct of this analysis is a detailed description of multiplication in the groupoid J¹G of one-jets of bisections of G.
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| ISSN: | 1815-0659 |