Stratifying endomorphism algebras using exact categories
type: Item
instance of: scholarly article
title: Stratifying endomorphism algebras using exact categories
zbMATH Open document ID: 1369.20004
author: Jie Du
author: Brian J. Parshall
author: Leonard L. Scott
published in: Journal of Algebra
publication date: 2017-02-28T00:00:00Z
review text: This paper is the second in a series aimed at proving versions of a conjecture made by the authors in 1996. The conjecture concerns the enlargement, in a framework involving Kazhdan-Lusztig cell theory, of those Hecke endomorphism algebras which occur naturally in the cross characteristic representation theory of finite groups of Lie type. See [the authors, J. Algebra 203, No. 1, 169--210 (1998; Zbl 0920.20008)] for the original version of the conjecture, and [the authors, Pac. J. Math. 279, No. 1--2, 229--254 (2015; Zbl 1365.20004)] for a reformulation. This paper under review constructs enlargements of Hecke algebras over \(\mathbb{Z}[t, t^{-1} ]\) to certain standardly stratified algebras. The latter are obtained as endomorphism algebras of modules with dual left cell module filtrations in the sense of Kazhdan-Lusztig. A novel feature of the proofs is the use of suitably chosen exact categories to avoid difficult \(\text{Ext}^1\)-vanishing conditions.
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 6690399
zbMATH Keywords: stratified algebra
zbMATH Keywords: Hecke algebra
zbMATH Keywords: left cell
zbMATH Keywords: endomorphism algebra
reviewed by: Feng Wei
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2016.11.002
OpenAlex ID: W2964205005
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DOI: 10.1016/J.JALGEBRA.2016.11.002
description: scientific article; zbMATH DE number 6690399