Projectively equivariant quantization and symbol on supercircle $S^{1|3}$

Bichr, Taher. "Projectively equivariant quantization and symbol on supercircle $S^{1|3}$." Czechoslovak Mathematical Journal 71.4 (2021): 1235-1248. <http://eudml.org/doc/297481>.

@article{Bichr2021,
abstract = {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 \} $, $ł\in \mathbb \{C\}$ 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.},
author = {Bichr, Taher},
journal = {Czechoslovak Mathematical Journal},
keywords = {differential operator; density; equivariant quantization and orthosymplectic algebra},
language = {eng},
number = {4},
pages = {1235-1248},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Projectively equivariant quantization and symbol on supercircle $S^\{1|3\}$},
url = {http://eudml.org/doc/297481},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Bichr, Taher
TI - Projectively equivariant quantization and symbol on supercircle $S^{1|3}$
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1235
EP - 1248
AB - 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 } $, $ł\in \mathbb {C}$ 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.
LA - eng
KW - differential operator; density; equivariant quantization and orthosymplectic algebra
UR - http://eudml.org/doc/297481
ER -