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Fixed rings in quotients of completed group rings

Research paper by William Woods

Indexed on: 16 Mar '19Published on: 07 Mar '19Published in: arXiv - Mathematics - Rings and Algebras



Abstract

Let $k$ be $\mathbb{F}_p$ or $\mathbb{Z}_p$, let $G$ be a compact $p$-adic analytic group, and form its completed group algebra $kG$. Take a closed subgroup $\Gamma$ of $G$. We analyse the structure of the fixed ring of $kG/I$ under the conjugation action of $\Gamma$, for certain ideals $I$ induced from the $G$-centraliser of $\Gamma$, and we explain the consequences this has for the theory of the prime ideals of $kG$.