TY - JOUR
T1 - Projective and conformal Schwarzian derivatives and cohomology of Lie algebras vector fields related to differential operators
AU - Bouarroudj, Sofiane
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2006/6
Y1 - 2006/6
N2 - Let M be either a projective manifold (M, Π) or a pseudo-Riemannian manifold (M, g). We extend, intrinsically, the projective/conformal Schwarzian derivatives we have introduced recently, to the space of differential operators acting on symmetric contravariant tensor fields of any degree on M. As operators, we show that the projective/conformal Schwarzian derivatives depend only on the projective connection Π and the conformal class of the metric [g], respectively. Furthermore, we compute the first cohomology group of Vect (M) with coefficients in the space of symmetric contravariant tensor fields valued in the space of δ-densities, and we compute the corresponding sl (n + 1, ℝ)-relative cohomology group.
AB - Let M be either a projective manifold (M, Π) or a pseudo-Riemannian manifold (M, g). We extend, intrinsically, the projective/conformal Schwarzian derivatives we have introduced recently, to the space of differential operators acting on symmetric contravariant tensor fields of any degree on M. As operators, we show that the projective/conformal Schwarzian derivatives depend only on the projective connection Π and the conformal class of the metric [g], respectively. Furthermore, we compute the first cohomology group of Vect (M) with coefficients in the space of symmetric contravariant tensor fields valued in the space of δ-densities, and we compute the corresponding sl (n + 1, ℝ)-relative cohomology group.
KW - Gelfand-Fuchs cohomology
KW - Invariant operators
KW - Projective/conformal structures
KW - The Schwarzian derivative
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U2 - 10.1142/S0219887806001338
DO - 10.1142/S0219887806001338
M3 - Article
AN - SCOPUS:33746304110
VL - 3
SP - 667
EP - 696
JO - International Journal of Geometric Methods in Modern Physics
JF - International Journal of Geometric Methods in Modern Physics
SN - 0219-8878
IS - 4
ER -