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Projectively equivariant quantization and symbol on supercircle $S^{1|3}$
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1235-1248
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Let $\mathcal {D}_{\lambda ,\mu } $ be the space of linear differential operators on weighted densities from $\mathcal {F}_{\lambda }$ to $\mathcal {F}_{\mu }$ as module over the orthosymplectic Lie superalgebra $\mathfrak {osp}(3|2)$, where $\mathcal {F}_{\lambda } $, $ł\in \nobreak \mathbb {C}$ is the space of tensor densities of degree $\lambda $ on the supercircle $S^{1|3}$. We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.\looseness -1
Let $\mathcal {D}_{\lambda ,\mu } $ be the space of linear differential operators on weighted densities from $\mathcal {F}_{\lambda }$ to $\mathcal {F}_{\mu }$ as module over the orthosymplectic Lie superalgebra $\mathfrak {osp}(3|2)$, where $\mathcal {F}_{\lambda } $, $ł\in \nobreak \mathbb {C}$ is the space of tensor densities of degree $\lambda $ on the supercircle $S^{1|3}$. We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.\looseness -1
DOI : 10.21136/CMJ.2021.0149-19
Classification : 17B10, 17B66, 53D10
Keywords: differential operator; density; equivariant quantization and orthosymplectic algebra 
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Bichr, Taher. Projectively equivariant quantization and symbol on supercircle $S^{1|3}$. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1235-1248. doi: 10.21136/CMJ.2021.0149-19

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