Noncommutative differential forms and quantization of the odd symplectic category

Details Noncommutative differential forms and quantization of the odd symplectic category Noncommutative differential forms and quantization of the odd symplectic category

2002-10-11

arxiv.org/abs/math/0210169v3

Mathematics

Quantum Algebra

4 pages; v2: minor changes

Scientific paper

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.

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