The projective class ring of basic and split Hopf algebras
type: Item
instance of: scholarly article
title: The projective class ring of basic and split Hopf algebras
zbMATH Open document ID: 0942.16039
DOI: 10.1023/A:1007703709638
author: Claude Cibils
published in: \(K\)-Theory
publication date: 2000-05-28T00:00:00Z
review text: The author considers finite dimensional Hopf algebras such that all the simple modules are 1-dimensional. The structure of the complexification of the projective class ring of such a Hopf algebra is described by using a positive integer determined by the composition series of the projective cover of the trivial module. If \(q\) is a root of unity of order \(n\), the projective class algebra of \(U_q^+({\mathfrak{sl}}_2)\) is the product of \(n-1\) copies of the dual numbers over \(\mathbb{C}\) and two copies of \(\mathbb{C}\).
reviewed by: Sorin Dascalescu
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 16D60
zbMATH DE Number: 1348190
zbMATH Keywords: finite dimensional Hopf algebras
zbMATH Keywords: half-quantum groups
zbMATH Keywords: projective class rings
zbMATH Keywords: simple modules
zbMATH Keywords: projective covers
MaRDI profile type: Publication
full work available at URL: a:1007703709638
OpenAlex ID: W2320255334
description: scientific article; zbMATH DE number 1348190