On deformation quantizations of symplectic supervarieties

TL;DR

This paper classifies deformation quantizations of smooth symplectic supervarieties, extending known results to the super case, and explores their relation to even reduced varieties and specific nilpotent orbits.

Contribution

It generalizes the classification of deformation quantizations to symplectic supervarieties and analyzes their relation to reduced varieties and nilpotent orbits.

Findings

Classification of deformation quantizations for smooth admissible symplectic supervarieties.

Relation established between quantizations of supervarieties and their even reduced counterparts.

Identification and classification of deformation quantizations for certain nilpotent orbits in Lie superalgebras.

Abstract

We classify deformation quantizations of the symplectic supervarieties that are smooth and admissible. This generalizes the corresponding result of Bezrukavnikov and Kaledin to the super case. We relate the equivalence classes of quantizations of supervarieties with that of their even reduced symplectic varieties. Finally, we prove that certain nilpotent orbits of basic Lie superalgebras are admissible and split, and classify their deformation quantizations.