Representation type of Schur algebras
type: Item
instance of: scholarly article
title: Representation type of Schur algebras
zbMATH Open document ID: 0942.16021
DOI: 10.1007/PL00004755
author: S. R. Doty
author: Karin Erdmann
author: S. Martin
author: Daniel K. Nakano
published in: Mathematische Zeitschrift
publication date: 1999-10-20T00:00:00Z
review text: The classification of the representation type of Schur algebras was initiated in the reviewer's papers [Can. J. Math. 44, No. 3, 665-672 (1992; Zbl 0776.20003) and J. Pure Appl. Algebra 84, No. 1, 73-84 (1993; Zbl 0795.16010)] and by \textit{K. Erdmann} [Q. J. Math., Oxf. II. Ser. 44, No. 173, 17-41 (1993; Zbl 0832.16011)]. In the first two papers the finite representation type of the Schur algebras \(S(n,r)\) with \(n\geq r\) was considered. The paper of Erdmann gave a complete determination of Schur algebras of finite representation type. In the present paper the authors give a complete classification of Schur algebras which are of tame type. Their classification shows that there are a few tame Schur algebras. As a second main result the authors present a full classification of infinitesimal Schur algebras of tame type. In this case the list is a little bit longer. Note that the infinitesimal Schur algebras of finite representation type were already determined by Doty, Nakano and Peters.
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 1351164
zbMATH Keywords: Schur algebras
zbMATH Keywords: representation types
zbMATH Keywords: symmetric groups
zbMATH Keywords: infinitesimal Schur algebras of tame type
Wikidata QID: Q116766134
reviewed by: Changchang Xi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1351164