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)
We study the prime ideal structure of the Iwasawa algebra G of an almost simple
compact p-adic Lie group G. When the Lie algebra of G contains a copy of the two-
dimensional non-abelian Lie algebra, we show that the prime ideal structure of G is
somewhat restricted. We also provide a potential example of a prime c-ideal of G in the
case when the Lie algebra of G is sl2(Qp).
Let p be a prime and let G be a compact p-adic Lie group. The Iwasawa algebra of G
G = Zp[[G]] := lim
is of interest in number theory and arithmetic geometry, particularly when G is an open
subgroup of GL2(Zp). When G is torsion free pro-p, G is also a concrete example of
a complete local (noncommutative in general) Noetherian integral domain with good
homological properties ().