 
Summary: #INVARIANT IDEALS IN IWASAWA ALGEBRAS
K. ARDAKOV, S. J. WADSLEY
Abstract. Let kG be the completed group algebra of a uniform prop group
G with coe#cients in a field k of characteristic p. We study right ideals I in
kG that are invariant under the action of another uniform prop group #. We
prove that if I is nonzero then an irreducible component of the characteristic
support of kG/I must be contained in a certain finite union of rational linear
subspaces of Spec gr kG. The minimal codimension of these subspaces gives a
lower bound on the homological height of I in terms of the action of a certain
Lie algebra on G/G p . If we take # to be G acting on itself by conjugation,
then #invariant right ideals of kG are precisely the twosided ideals of kG, and
we obtain a nontrivial lower bound on the homological height of a possible
nonzero twosided ideal. For example, when G is open in SLn (Zp ) this lower
bound equals 2n  2. This gives a significant improvement of the results of
Ardakov, Wei and Zhang [AWZ1] on reflexive ideals in Iwasawa algebras.
1. Introduction
1.1. Prime ideals in Iwasawa algebras. In recent years, several attempts have
been made to understand the structure of prime ideals in noncommutative Iwasawa
algebras. These are the completed group
algebras# G of compact padic analytic
