AN EXPLICIT FORMULA FOR PBW QUANTIZATION

ABSTRACT

Let k be a field of characteristic zero, a k-Lie algebra, the symmetrization map. The PBW quantization is the one parameter family of associative products:

where is the homogeneous component of degree of the map , . In this paper we give an explicit formula for B. As an application, we prove that for each , is a bidifferential operator of order .

ACKNOWLEDGMENTS

I wish to thank Boris Tsygan, from whom I learned of the relation between the Campbell-Hausdorff series and the . Victor Ginzburg told me that no general formula as I was looking for seemed to be known. His comment encouraged me to carry out this research, and I am thankful to him for it. Thanks also to Alexei Davydov for a useful discussion.

Partially supported by grants BID802/OC-AR-PICT 2260 and UBACyT TW79. This research was carried out while visiting the universities of Bielefeld and Münster with a Humboldt fellowship.