Gamma-invariant ideals in Iwasawa algebras
| dc.creator | Ardakov, K. | |
| dc.creator | Wadsley, S. J. | |
| dc.date | 2008-08-17 | |
| dc.date.accessioned | 2026-07-07T09:57:06Z | |
| dc.date.available | 2026-07-07T09:57:06Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0808.2311 | |
| dc.identifier | http://arxiv.org/abs/0808.2311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167219 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16L30, 16P40 | |
| dc.title | Gamma-invariant ideals in Iwasawa algebras | |
| dc.type | text |