an:00934775
Zbl 0866.58037
Karabegov, Alexander V.
Deformation quantizations with separation of variables on a K??hler manifold
EN
Commun. Math. Phys. 180, No. 3, 745-755 (1996).
00035980
1996
j
53D50 81S10 53B35
deformation quantization; K??hler manifolds; separation of variables
A deformation quantization on a symplectic manifold \(M\) is an associative algebra structure on the space \(C^\infty(M)[[v]]\) of formal power series such that the algebra multiplication * is a deformation of the ordinary multiplication of functions on \(M\) and the *-commutator is a deformation of the Poisson bracket. In this paper the author considers deformation quantizations on K??hler manifolds that satisfy the following separation of variables property. For each open set \(U\subseteq M\) the *-multiplication from the left by a holomorphic function and from the right by an antiholomorphic function coincides with the ordinary multiplication. He shows that these quantizations are in 1-1 correspondence with the formal deformations of the original K??hler metric.
V.Perlick (Berlin)