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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147129 |
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| Zitieren: | 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| _version_ | 1862665347413311488 |
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| author | Mehta, R.A. |
| author_facet | Mehta, R.A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T15:16:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147129 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:16:36Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Modular Classes of Lie Groupoid Representations up to Homotopy Mehta, R.A. |
| title | 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_short | Modular Classes of Lie Groupoid Representations up to Homotopy |
| title_sort | modular classes of lie groupoid representations up to homotopy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147129 |
| work_keys_str_mv | AT mehtara modularclassesofliegroupoidrepresentationsuptohomotopy |