A criterion for quasi-hereditary, and an abstract straightening formula
type: Item
instance of: scholarly article
title: A criterion for quasi-hereditary, and an abstract straightening formula
zbMATH Open document ID: 0887.16012
published in: Inventiones Mathematicae
publication date: 1998-03-16T00:00:00Z
review text: The author provides a criterion to see whether an algebra is quasi-hereditary. (Of course, this is a very interesting question.) The main point is that the criterion given by the author uses an integral version of the given algebra. Thus he imposes conditions not on the given algebra itself, but on its integral version and a certain semisimple algebra which contains the given one. The condition is, roughly speaking, a straightening formula for a formal character of the semisimple algebra. By applying his criterion to many important algebras, he gets a unified proof of the quasi-heredity of Schur algebras, generalized Schur algebras, \(q\)-Schur algebras and the Temperley-Lieb algebras of type \(A\) and \(B\) with non-zero parameters, (for these algebras, the known quasi-heredity was proved by many other authors using different methods).
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 20C10
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 1026421
zbMATH Keywords: Schur algebras
zbMATH Keywords: hereditary ideals
zbMATH Keywords: quasi-hereditary algebras
zbMATH Keywords: straightening formulas
zbMATH Keywords: semisimple algebras
zbMATH Keywords: quasi-heredity
author: Steffen Koenig
reviewed by: Changchang Xi
MaRDI profile type: Publication
full work available at URL: s002220050128
OpenAlex ID: W1982922921
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DOI: 10.1007/S002220050128
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description: scientific article; zbMATH DE number 1026421