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
G
L
q
(n)
, or its restrictions to
S
L
q
(n)
,
U
q
(n)
and
S
U
q
(n)
. The quantum Yang-Baxter equation for R holds because of the Hecke relation for the braiding matrix of the homogeneous subgroup. A bicovariant differential calculus on
IG
L
q
(n)
is constructed, and its application to the
D=4
Poincaré group $ISL_q(2,\Cb)$ is discussed.