Reference : On a Lie Algebraic Characterization of Vector Bundles
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/112830
On a Lie Algebraic Characterization of Vector Bundles
English
Lecomte, Pierre mailto [Université de Liège - ULg > Département de mathématique > Géométrie et théorie des algorithmes >]
Leuther, Thomas mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Dép. d'électric., électron. et informat. (Inst.Montefiore) >]
Zihindula Mushengezi, Elie mailto [Université de Liège - ULg > Département de mathématique > Géométrie et théorie des algorithmes >]
26-Jan-2012
Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA]
Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine
SIGMA 8 (2012)
Yes (verified by ORBi)
International
1815-0659
Kiev
Ukraine
[en] vector bundle ; algebraic characterization ; differential operators
[en] We prove that a vector bundle 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 ibration 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.
http://hdl.handle.net/2268/112830
10.3842/SIGMA.2012.004
http://www.emis.de/journals/SIGMA/2012/004/sigma12-004.pdf

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
sigma12-004.pdfPublisher postprint322.78 kBView/Open

Bookmark and Share SFX Query

All documents in ORBi are protected by a user license.