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...
Збережено в:
| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148549 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
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irk-123456789-1485492019-02-19T01:24:21Z Cartan Connections on Lie Groupoids and their Integrability Blaom, A.D. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148549 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Blaom, A.D. |
| spellingShingle |
Blaom, A.D. Cartan Connections on Lie Groupoids and their Integrability Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Blaom, A.D. |
| author_sort |
Blaom, A.D. |
| title |
Cartan Connections on Lie Groupoids and their Integrability |
| title_short |
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_sort |
cartan connections on lie groupoids and their integrability |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148549 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT blaomad cartanconnectionsonliegroupoidsandtheirintegrability |
| first_indexed |
2023-05-20T17:29:43Z |
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2023-05-20T17:29:43Z |
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1796153420449579008 |