The Serre relations in Ringel-Hall algebras
type: Item
instance of: scholarly article
title: The Serre relations in Ringel-Hall algebras
zbMATH Open document ID: 1019.17004
DOI: 10.1142/S0252959902000328
author: Abdukader Obul
published in: Chinese Annals of Mathematics. Series B
publication date: 2003-09-21T00:00:00Z
review text: The author first constructs the Casimir element of the Hall algebra. Applying the method of the Gabber-Kac theorem, it is proved that the Serre relations are the defining relations of the composition algebra. From this point of view, the Ringel-Green isomorphism theorem still holds for standard composition algebras. This means that the Drinfeld double of a composition algebra with an indeterminate \(v\) is naturally isomorphic to the quantum groups in the sense of Drinfeld-Jimbo.
reviewed by: Fang Li
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1833169
zbMATH Keywords: Hall algebra
zbMATH Keywords: composition algebra
zbMATH Keywords: Casimir element
zbMATH Keywords: Serre relation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1833169