Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds
In the paper under review super Toeplitz operators are used to construct quantization deformations of the algebras of functions on complex supermanifolds. The resulting algebras may be regarded as algebras of ``quantized functions'' in the sense of Connes's noncommutative geometry. The semi-classical limits of these deformations correspond to super Poisson structures. The paper does not develop a general theory, but rather deals with two specific examples, namely, the trivial (1,1) dimensional supermanifold over the unit disk in \(\mathbb{C}\), and the trivial \((m,n)\) dimensional supermanifold based on \(\mathbb{C}^ m\).
scientific article; zbMATH DE number 221171
scientific article