Dominant and global dimension of blocks of quantised Schur algebras
type: Item
instance of: scholarly article
title: Dominant and global dimension of blocks of quantised Schur algebras
zbMATH Open document ID: 1498.18016
author: Ming Fang
author: Wei Hu
author: Steffen Koenig
published in: Mathematische Zeitschrift
publication date: 2022-01-25T00:00:00Z
review text: Schur algebras and quantised (or \(q\)-) Schur algebras have been fundamental objects in representation theory since its early days. In the paper under review, the authors give explicit formulae for the dominant and the global dimension of indecomposable blocks of \(S(n,r)\) and \(S_q(n,r)\) with \(n\geq r\). The main methods used in the proofs come from the derived equivalences constructed by the authors [J. Reine Angew. Math. 770, 59--85 (2021; Zbl 1472.18008)]. As an application, it is shown that two blocks \(B\) and \(B'\) of Schur algebras \(S_q(n,r)\) for \(n\geq r\) and \(S_q(n',r')\) for \(n'\geq r'\), respectively, are derived equivalent if and only if they have the same global dimension.
reviewed by: Shengyong Pan
Mathematics Subject Classification ID: 18G80
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 20G43
zbMATH DE Number: 7463798
zbMATH Keywords: dominant dimension
zbMATH Keywords: global dimension
zbMATH Keywords: Schur algebras
zbMATH Keywords: derived equivalences
MaRDI profile type: Publication
full work available at URL: s00209-021-02792-w
OpenAlex ID: W3176809635
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DOI: 10.1007/S00209-021-02792-W
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description: scientific article; zbMATH DE number 7463798