 
Summary: Under consideration for publication in Math. Proc. Camb. Phil. Soc. 1
Prime ideals in noncommutative Iwasawa algebras
By KONSTANTIN ARDAKOV
Christ's College, Cambridge CB2 3BU
(Received July 2004)
Abstract
We study the prime ideal structure of the Iwasawa algebra G of an almost simple
compact padic Lie group G. When the Lie algebra of G contains a copy of the two
dimensional nonabelian Lie algebra, we show that the prime ideal structure of G is
somewhat restricted. We also provide a potential example of a prime cideal of G in the
case when the Lie algebra of G is sl 2 (Q p ).
1. Introduction
Let p be a prime and let G be a compact padic Lie group. The Iwasawa algebra of G
G = Z p [[G]] := lim N/oGZ p [G=N ]
is of interest in number theory and arithmetic geometry, particularly when G is an open
subgroup of GL 2 (Z p ). When G is torsion free prop, G is also a concrete example of
a complete local (noncommutative in general) Noetherian integral domain with good
homological properties ([10]).
Recently, J. Coates, P. Schneider and R. Sujatha ([5]) developed a structure theory for
nitely generated modules over G . One of the main features of this theory is the notion
