On the Iwasawa algebra for pro-l Galois groups

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 (a) and are finite. We give a full description of the algebraic structure of the semisimple algebra for pro-l Galois groups G with [[G]] the Iwasawa algebra. We moreover compute the cohomological dimension of the centres of the Wedderburn components of and state some results on the completion of .