• Corpus ID: 141439761

Conformally equivariant quantization and symbol maps associated with $n$-ary differential operators on weighted densities

@article{Boujelben2019ConformallyEQ,
title={Conformally equivariant quantization and symbol maps associated with \$n\$-ary differential operators on weighted densities},
author={Jamel Boujelben and Taher Bichr and K. Tounsi},
journal={arXiv: Differential Geometry},
year={2019}
}
• Published 30 April 2019
• Mathematics
• arXiv: Differential Geometry
We are interested in the study of the space of $n$-ary differential operators denoted by $\mathfrak{D}_{\underlinel,\mu}$ where $\underlinel=(l_{1},...,l_{n})$ acting on weighted densities from $\frak F_{l_1}\otimes\frak F_{l_2}\otimes...\otimes\frak F_{l_n}$ to $\frak F_{\mu}$ as a module over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$. As a consequence, we prove the existence and the uniqueness of a canonical conformally equivariant symbol map from $\mathfrak{D}_{\underline… References SHOWING 1-10 OF 25 REFERENCES • Mathematics • 2013 We consider the space of differential operators$\mathcal{D}_{\lambda\mu}$acting between$\lambda$- and$\mu$-densities defined on$S^{1|2}$endowed with its standard contact structure. This contact • Mathematics • 2013 Over the$(1,n)$-dimensional real supercircle, we consider the$\mathcal{K}(n)$-modules of linear differential operators,$\frak{D}^n_{\lambda,\mu}$, acting on the superspaces of weighted densities, • Mathematics • 1998 AbstractThe spaces of linear differential operators $$D_\lambda (\mathbb{R}^n )$$ acting on λ-densities on $$\mathbb{R}^n$$ and the space $${\text{Pol(}}T^* \mathbb{R}^n {\text{)}}$$ of • Mathematics • 2010 We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra $${\mathfrak{pgl}(p+1|q)}$$ is simple, our result AbstractIn this Letter, we show the existence of a natural and projectively equivariant quantization map depending on a linear torsion-free connection for the spaces${\cal D}_p(M)\$ of differential
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We consider the supercircle S1|1 equipped with the standard contact structure. The Lie superalgebra $${\fancyscript{K}(1)}$$ of contact vector fields contains the Möbius superalgebra osp(1|2). We
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AbstractThe space $$D^k$$ of kth-order linear differential operators on $$\mathbb{R}$$ is equipped with a natural two-parameter family of structures of Diff( $$\mathbb{R}$$ )-modules. To specify
• Mathematics
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The concept of conformally equivariant quantization was introduced by C. Duval, P. Lecomte and V. Ovsienko for manifolds endowed with flat conformal structures. They obtained results of existence and
• Mathematics
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A quantization can be seen as a way to construct a differential operator with prescribed principal symbol. The map from the space of symbols to the space of differential operators is moreover