\(R\)-Hopf algebra orders in \(KC_{p^ 2}\)
type: Item
instance of: scholarly article
title: \(R\)-Hopf algebra orders in \(KC_{p^ 2}\)
zbMATH Open document ID: 0820.16036
published in: Journal of Algebra
publication date: 1995-09-12T00:00:00Z
review text: Let \(K\) be a finite extension field of the \(p\)-adic rationals and let \(R\) be the integral closure of the \(p\)-adic integers in \(K\). For any finite group \(G\), the group algebra \(KG\) is a Hopf algebra, and an \(R\)-order in \(KG\) is said to be a Hopf order if it inherits a Hopf algebra structure from \(KG\). In the case that \(G = C_ p\) is cyclic of order \(p\), Larson has described all the \(R\)-Hopf orders in \(KC_ p\), and this construction was extended by Greither to obtain some types of \(R\)-Hopf order in \(KC_{p^ 2}\). In the present paper, the author uses Larson's results, together with ingenious computations, to complete the description of \(R\)- orders in \(KC_{p^ 2}\): any such order is either a Greither order or the linear dual of a Greither order.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 682580
zbMATH Keywords: finite groups
zbMATH Keywords: group algebras
zbMATH Keywords: Hopf algebras
zbMATH Keywords: \(R\)-Hopf orders
zbMATH Keywords: Greither orders
author: Robert G. Underwood
MaRDI profile type: Publication
full work available at URL: jabr.1994.1293
OpenAlex ID: W2081096377
DOI: 10.1006/JABR.1994.1293
description: scientific article; zbMATH DE number 682580