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Higher Symmetries of the conformal Laplacian Radoux, Fabian Conference (2014, July 14) Detailed reference viewed: 10 (0 ULg)Higher Symmetries of the conformal Laplacian Radoux, Fabian Conference (2014, June 09) Detailed reference viewed: 4 (0 ULg)SECOND ORDER SYMMETRIES OF THE CONFORMAL LAPLACIAN Michel, Jean-Philippe ; Radoux, Fabian ; in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2014), 10(016), 26 Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by ... [more ▼] Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order. They are constructed from conformal Killing 2-tensors satisfying a natural and conformally invariant condition. As a consequence, we get also the classification of the second order symmetries of the conformal Laplacian. Our results generalize the ones of Eastwood and Carter, which hold on conformally flat and Einstein manifolds respectively. We illustrate our results on two families of examples in dimension three. [less ▲] Detailed reference viewed: 23 (1 ULg)Higher symmetries of the conformal Laplacian Radoux, Fabian Scientific conference (2013, December 10) Detailed reference viewed: 13 (0 ULg)Quantifications équivariantes Radoux, Fabian Scientific conference (2013, November 05) Detailed reference viewed: 5 (0 ULg)Higher symmetries of the conformal Laplacian Radoux, Fabian Scientific conference (2013, July 30) Detailed reference viewed: 4 (1 ULg)Higher symmetries of the conformal Laplacian Radoux, Fabian Conference (2013, May 29) Detailed reference viewed: 5 (1 ULg)Geodesics on a supermanifold and projective equivalence of superconnections Leuther, Thomas ; Radoux, Fabian ; in Journal of Geometry & Physics (2013), 67 Detailed reference viewed: 31 (1 ULg)spo(2|2)-equivariant quantizations on the supercircle S^{1|2} ; ; Radoux, Fabian in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2013), 9(055), 17 Detailed reference viewed: 23 (5 ULg)Quantifications équivariantes Radoux, Fabian Scientific conference (2012, March 15) Detailed reference viewed: 21 (1 ULg)On osp(p+1,q+1|2r)-equivariant quantizations Leuther, Thomas ; Mathonet, Pierre ; Radoux, Fabian in Journal of Geometry & Physics (2012), 62 Detailed reference viewed: 38 (12 ULg)Equivariant quantization in supergeometry Radoux, Fabian Scientific conference (2011, December 08) Detailed reference viewed: 18 (8 ULg)Projectively equivariant quantization over R^{p|q} Radoux, Fabian Conference (2011, September 13) Detailed reference viewed: 11 (2 ULg)Natural and invariant quantizations Radoux, Fabian Conference (2011, July 12) Detailed reference viewed: 10 (2 ULg)Quantifications équivariantes Radoux, Fabian Scientific conference (2011, April 15) Detailed reference viewed: 22 (4 ULg)Quantifications naturelles projectivement équivariantes Radoux, Fabian Book published by Editions Universitaires Européennes (2011) Detailed reference viewed: 25 (3 ULg)Natural and Projectively Invariant Quantizations on Supermanifolds Leuther, Thomas ; Radoux, Fabian in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2011) The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using ... [more ▼] The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two. [less ▲] Detailed reference viewed: 48 (18 ULg)Quantifications équivariantes Radoux, Fabian Scientific conference (2011, March 28) Detailed reference viewed: 13 (3 ULg)Quantifications équivariantes Radoux, Fabian Scientific conference (2011, January 27) Detailed reference viewed: 17 (4 ULg)Projectively equivariant quantizations over the superspace R^{p|q} Mathonet, Pierre ; Radoux, Fabian in Letters in Mathematical Physics (2011), 98(3), 311-331 We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the ... [more ▼] We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields. [less ▲] Detailed reference viewed: 34 (16 ULg) |
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