A h-adic valuation property of universal R-matrices

Abstract

We prove that if U_h(g) is a quasitriangular QUE algebra with universal R-matrix R, and O_h(G^*) is the quantized function algebra sitting inside U_h(g), then h log(R) belongs to the tensor square O_h(G^*) otimes O_h(G^*). This gives another proof of the results of Gavarini and Halbout, saying that R normalizes O_h(G^*) otimes O_h(G^*) and therefore induces a braiding of the formal group G^* (in the sense of Weinstein and Xu, or Reshetikhin).