On a Lie Algebraic Characterization of Vector Bundles
We prove that a vector bundle π: E→M is characterized by the Lie algebra generated by all differential operators on E which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole f...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148364 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On a Lie Algebraic Characterization of Vector Bundles / P. B.A. Lecomte, T. Leuther, E.Z. Mushengezi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712227128147968 |
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| author | B.A. Lecomte, P. Leuther, T. Mushengezi, E.Z. |
| author_facet | B.A. Lecomte, P. Leuther, T. Mushengezi, E.Z. |
| citation_txt | On a Lie Algebraic Characterization of Vector Bundles / P. B.A. Lecomte, T. Leuther, E.Z. Mushengezi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove that a vector bundle π: E→M is characterized by the Lie algebra generated by all differential operators on E which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole fibration that is characterized here. The proof relies on a theorem of [Lecomte P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same hypotheses. In particular, our characterization holds only for vector bundles of rank greater than 1.
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| first_indexed | 2025-12-07T17:35:29Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148364 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:35:29Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | B.A. Lecomte, P. Leuther, T. Mushengezi, E.Z. 2019-02-18T11:00:40Z 2019-02-18T11:00:40Z 2012 On a Lie Algebraic Characterization of Vector Bundles / P. B.A. Lecomte, T. Leuther, E.Z. Mushengezi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 8 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 13N10; 16S32; 17B65; 17B63 DOI: http://dx.doi.org/10.3842/SIGMA.2012.004 https://nasplib.isofts.kiev.ua/handle/123456789/148364 We prove that a vector bundle π: E→M is characterized by the Lie algebra generated by all differential operators on E which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole fibration that is characterized here. The proof relies on a theorem of [Lecomte P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same hypotheses. In particular, our characterization holds only for vector bundles of rank greater than 1. We thank the referees for suggestions leading to improvements of the original paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On a Lie Algebraic Characterization of Vector Bundles Article published earlier |
| spellingShingle | On a Lie Algebraic Characterization of Vector Bundles B.A. Lecomte, P. Leuther, T. Mushengezi, E.Z. |
| title | On a Lie Algebraic Characterization of Vector Bundles |
| title_full | On a Lie Algebraic Characterization of Vector Bundles |
| title_fullStr | On a Lie Algebraic Characterization of Vector Bundles |
| title_full_unstemmed | On a Lie Algebraic Characterization of Vector Bundles |
| title_short | On a Lie Algebraic Characterization of Vector Bundles |
| title_sort | on a lie algebraic characterization of vector bundles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148364 |
| work_keys_str_mv | AT balecomtep onaliealgebraiccharacterizationofvectorbundles AT leuthert onaliealgebraiccharacterizationofvectorbundles AT mushengeziez onaliealgebraiccharacterizationofvectorbundles |