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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148549 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862570159052423168 |
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| author | Blaom, A.D. |
| author_facet | Blaom, A.D. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-11-26T02:07:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148549 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T02:07:04Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blaom, A.D. 2019-02-18T15:14:02Z 2019-02-18T15:14:02Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 53C05; 58H05; 53C07 DOI:10.3842/SIGMA.2016.114 https://nasplib.isofts.kiev.ua/handle/123456789/148549 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Cartan Connections on Lie Groupoids and their Integrability Article published earlier |
| spellingShingle | Cartan Connections on Lie Groupoids and their Integrability Blaom, A.D. |
| title | Cartan Connections on Lie Groupoids and their Integrability |
| title_full | Cartan Connections on Lie Groupoids and their Integrability |
| title_fullStr | Cartan Connections on Lie Groupoids and their Integrability |
| title_full_unstemmed | Cartan Connections on Lie Groupoids and their Integrability |
| title_short | Cartan Connections on Lie Groupoids and their Integrability |
| title_sort | cartan connections on lie groupoids and their integrability |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148549 |
| work_keys_str_mv | AT blaomad cartanconnectionsonliegroupoidsandtheirintegrability |