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Natural and Projectively Invariant Quantizations on Supermanifolds
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathfrak{pgl}({n+1|m})$-equivariant quantization on ${\mathbb{R}}^{n|m}$ 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.
Keywords: supergeometry; differential operators; projective invariance; quantization maps. 
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Thomas Leuther; Fabian Radoux. Natural and Projectively Invariant Quantizations on Supermanifolds. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a33/

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