Abstract
This article begin with an attempt to understand the work of Kontsevich and Fukaya on the Mirror Symmetry conjecture and homological string model. We define the super deformation quantizations of the super structure sheaf of a supermanifold. We study the super deformation quantizations of the tangent space of extended moduli on the homological superstring B-model. Our main conjecture is that the superdifferential graded Lie algebra will be deformation quantizable. This is a supergeometric generalization of Omori’s challenged result.
