Deformation quantization of Poisson manifolds. (English) Zbl 1058.53065

Kontsevich, Maxim

Lett. Math. Phys. 66, No. 3, 157-216 (2003).

The author proves that any finite-dimensional Poisson manifold can be canonically quantized in the sense of deformation quantization. The solution presented here uses in an essential way some ideas of string theory. The author’s formulas can be viewed as a perturbation series for a topological 2-dimensional quantum field theory coupled with gravity.
This important article circulated since 1997 as a frequently cited preprint (q-alg/9709040).

Reviewer: Mircea Puta (Timişoara)

MSC:

53D55	Deformation quantization, star products
16E40	(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
18G55	Nonabelian homotopical algebra (MSC2010)
53D17	Poisson manifolds; Poisson groupoids and algebroids
81S10	Geometry and quantization, symplectic methods

Keywords:

deformation quantization; homotopy Lie algebra