Coherence of augmented Iwasawa algebras
نویسندگان
چکیده
The augmented Iwasawa algebra of a p-adic Lie group is generalisation the compact group. We prove that split-semisimple over field has coherent if and only its root system rank one. deduce general linear degree n precisely when at most two. also characterise certain solvable groups have algebra.
منابع مشابه
Reflexive Ideals in Iwasawa Algebras
Let G be a torsionfree compact p-adic analytic group. We give sufficient conditions on p and G which ensure that the Iwasawa algebra ΩG of G has no non-trivial two-sided reflexive ideals. Consequently, these conditions imply that every nonzero normal element in ΩG is a unit. We show that these conditions hold in the case when G is an open subgroup of SL2(Zp) and p is arbitrary. Using a previous...
متن کاملHybrid Iwasawa Algebras and the Equivariant Iwasawa Main Conjecture
Let p be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for an infinite class of one-dimensional non-abelian p-adic Lie extensions. Crucially, this result does not depend on the vanishing of the relevant Iwasawa μ-invariant.
متن کاملNonexistence of Reflexive Ideals in Iwasawa Algebras of Chevalley Type
Let Φ be a root system and let Φ(Zp) be the standard Chevalley Zp-Lie algebra associated to Φ. For any integer t > 1, let G be the uniform pro-p group corresponding to the powerful Lie algebra pΦ(Zp) and suppose that p > 5. Then the Iwasawa algebra ΩG has no nontrivial reflexive ideals. This was previously proved by authors for the root system A1.
متن کاملamenability of banach algebras
chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...
15 صفحه اولEisenstein Hecke Algebras and Conjectures in Iwasawa Theory
We formulate a weak Gorenstein property for the Eisenstein component of the p-adic Hecke algebra associated to modular forms. We show that this weak Gorenstein property holds if and only if a weak form of Sharifi’s conjecture and a weak form of Greenberg’s conjecture hold.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2023
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2023.108916