R matrix and bicovariant calculus for the inhomogeneous quantum groups IGL q( n)

Abstract

We find the R matrix for the inhomogeneous quantum groups whose homogeneous part is GL q ( n), or its restrictions to SL q ( n), U q ( n) and SU q ( n). The quantum Yang-Baxter equation for R holds because of the Hecke relation for the braiding matrix of homogeneous subgroup. A bicovariant differential calculus on IGL q ( n) is constructed, and its application to the D = 4 Poincaré group ISL q(2, C) is discussed.