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On a Lie Algebraic Characterization of Vector Bundles
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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On a Lie Algebraic Characterization of Vector Bundles
Інший ID:
2010 Mathematics Subject Classification: 13N10; 16S32; 17B65; 17B63
DOI: http://dx.doi.org/10.3842/SIGMA.2012.004
DOI: http://dx.doi.org/10.3842/SIGMA.2012.004
Посилання:
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.
Підтримка:
We thank the referees for suggestions leading to improvements of the original paper.
Дата:
2012
Переглядів:
615
Завантажень:
240
Анотація:
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.
