  Let l be an odd prime and K/k a Galois extension of totally real number
fields with Galois group G such that K/k_\infty and k/Q are finite. We give a
full description of the algebraic structure of the semisimple algebra
QG=Quot(\Lambda G) for pro-l Galois groups G with \Lambda G = Z_l[[G]] the
Iwasawa algebra. We moreover compute the cohomological dimension of the centres
of the Wedderburn components of QG and state some results on the completion of
QG.
