  There is a simple and natural quantization of differential forms on odd
Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two
functions f and g. We notice that this non-commutative differential algebra has
a geometrical realization as a convolution algebra of the symplectic groupoid
integrating the Poisson manifold.
  This quantization is just a part of a quantization of the odd symplectic
category (where objects are odd symplectic supermanifolds and morphisms are
Lagrangian relation) in terms of Z_2-graded chain complexes. It is a
straightforward consequence of the theory of BV operator acting on
semidensities, due to H. Khudaverdian.

Quantum Algebra;High Energy Physics - Theory;Symplectic Geometry