Modular Classes of Lie Groupoid Representations up to Homotopy
We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein's ''The volume of a dif...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147129 |
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| Cite this: | Modular Classes of Lie Groupoid Representations up to Homotopy / R.A. Mehta // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Mehta, R.A. 2019-02-13T17:11:15Z 2019-02-13T17:11:15Z 2015 Modular Classes of Lie Groupoid Representations up to Homotopy / R.A. Mehta // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 22A22; 53D17 DOI:10.3842/SIGMA.2015.051 https://nasplib.isofts.kiev.ua/handle/123456789/147129 We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein's ''The volume of a differentiable stack''. This paper is a contribution to the Special Issue on Poisson Geometry in Mathematics and Physics. The full collection is available at http://www.emis.de/journals/SIGMA/Poisson2014.html. We thank Ping Xu for helpful comments on a draft of the paper. We also thank the referees for many useful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Modular Classes of Lie Groupoid Representations up to Homotopy Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Modular Classes of Lie Groupoid Representations up to Homotopy |
| spellingShingle |
Modular Classes of Lie Groupoid Representations up to Homotopy Mehta, R.A. |
| title_short |
Modular Classes of Lie Groupoid Representations up to Homotopy |
| title_full |
Modular Classes of Lie Groupoid Representations up to Homotopy |
| title_fullStr |
Modular Classes of Lie Groupoid Representations up to Homotopy |
| title_full_unstemmed |
Modular Classes of Lie Groupoid Representations up to Homotopy |
| title_sort |
modular classes of lie groupoid representations up to homotopy |
| author |
Mehta, R.A. |
| author_facet |
Mehta, R.A. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein's ''The volume of a differentiable stack''.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147129 |
| citation_txt |
Modular Classes of Lie Groupoid Representations up to Homotopy / R.A. Mehta // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 14 назв. — англ. |
| work_keys_str_mv |
AT mehtara modularclassesofliegroupoidrepresentationsuptohomotopy |
| first_indexed |
2025-12-07T15:16:36Z |
| last_indexed |
2025-12-07T15:16:36Z |
| _version_ |
1850863094979362816 |