Finite groups with semisimple endomorphism rings

Modules with Dedekind Finite Endomorphism Rings

This article is a survey of modules whose endomorphism rings are Dedekind finite, Hopfian or co-Hopfian. We summarise the properties of such modules and present unified proofs of known results and generalisations to new structure theorems. MSC 2010. 16S50, 16D80.

Endomorphism rings of almost full formal groups

Let oK be the integral closure of Zp in a finite field extension K of Qp, and let F be a one-dimensional full formal group defined over oK . We study certain finite subgroups C of F and prove a conjecture of Jonathan Lubin concerning the absolute endomorphism ring of the quotient F/C when F has height 2. We also investigate ways in which this result can be generalized to p-adic formal groups of...

Representing Finite Groups: A Semisimple Introduction

Endomorphism Rings in Cryptography

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Homological Properties of Quantized Coordinate Rings of Semisimple Groups

We prove that the generic quantized coordinate ringOq(G) is Auslander-regular, Cohen-Macaulay, and catenary for every connected semisimple Lie group G. This answers questions raised by Brown, Lenagan, and the first author. We also prove that under certain hypotheses concerning the existence of normal elements, a noetherian Hopf algebra is Auslander-Gorenstein and Cohen-Macaulay. This provides a...