2008/08/17 by Konstantin Ardakov, K. Ardakov, Ardakov, K. +3
Mathematics · #16L30 #16P40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16L30 #msc:16P40
paper · pdf · doi:10.48550/arxiv.0808.2311
arxiv created 2008/08/17 · openalex publication_date 2008/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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/Gp. 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 SLn(\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.