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Sur la caractérisation (Lie-)algébrique des fibrés et des variétés différentielles Zihindula Mushengezi, Elie Doctoral thesis (2013) Detailed reference viewed: 97 (12 ULg)On a Lie Algebraic Characterization of Vector Bundles Lecomte, Pierre ; Leuther, Thomas ; Zihindula Mushengezi, Elie in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2012) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 58 (10 ULg) |
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