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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dc.contributor.author	B.A. Lecomte, P.
dc.contributor.author	Leuther, T.
dc.contributor.author	Mushengezi, E.Z.
dc.date.accessioned	2019-02-18T11:00:40Z
dc.date.available	2019-02-18T11:00:40Z
dc.date.issued	2012
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 13N10; 16S32; 17B65; 17B63
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2012.004
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148364
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	We thank the referees for suggestions leading to improvements of the original paper.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	On a Lie Algebraic Characterization of Vector Bundles	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA