Gamma-invariant ideals in Iwasawa algebras

Let kG be the completed group algebra of a uniform pro-p group G with coefficients in a field k of characteristic p. We study right ideals I in kG that are invariant under the action of another uniform pro-p group Gamma. We prove that if I is non-zero 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 Gamma to be G acting on itself by conjugation, then Gamma-invariant right ideals of kG are precisely the two-sided ideals of kG, and we obtain a non-trivial lower bound on the homological height of a possible non-zero two-sided ideal. For example, when G is open in SL_n(\Zp) this lower bound equals 2n - 2. This gives a significant improvement of the results of Ardakov, Wei and Zhang on reflexive ideals in Iwasawa algebras

Star Formation in Disk Galaxies. III. Does stellar feedback result in cloud death?

Stellar feedback, star formation and gravitational interactions are major controlling forces in the evolution of Giant Molecular Clouds (GMCs). To explore their relative roles, we examine the properties and evolution of GMCs forming in an isolated galactic disk simulation that includes both localised thermal feedback and photoelectric heating. The results are compared with the three previous simulations in this series which consists of a model with no star formation, star formation but no form of feedback and star formation with photoelectric heating in a set with steadily increasing physical effects. We find that the addition of localised thermal feedback greatly suppresses star formation but does not destroy the surrounding GMC, giving cloud properties closely resembling the run in which no stellar physics is included. The outflows from the feedback reduce the mass of the cloud but do not destroy it, allowing the cloud to survive its stellar children. This suggests that weak thermal feedback such as the lower bound expected for supernova may play a relatively minor role in the galactic structure of quiescent Milky Way-type galaxies, compared to gravitational interactions and disk shear.Comment: 15 pages, 15 figures, accepted for publication in Ap