A h-adic valuation property of universal R-matrices

Details A h-adic valuation property of universal R-matrices A h-adic valuation property of universal R-matrices

2002-04-18

arxiv.org/abs/math/0204227v1

J. Algebra 261 (2003), no. 2, 434-447

Mathematics

Quantum Algebra

14 pages

Scientific paper

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).

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