Quantization of formal classical dynamical r-matrices: the reductive case

Abstract

In this paper we prove the existence of a formal dynamical twist quantization for any triangular and non-modified formal classical dynamical $r$-matrix in the reductive case. The dynamical twist is constructed as the image of the dynamical $r$-matrix by a $L_{\infty }$-quasi-isomorphism. This quasi-isomorphism also allows us to classify formal dynamical twist quantizations up to gauge equivalence.

13 pages, 1 section added (classification of dynamical twists), LaTeX, final version, to appear in Adv. Math