Cohomological stratification of diagram algebras.
type: Item
instance of: scholarly article
title: Cohomological stratification of diagram algebras.
zbMATH Open document ID: 1198.16010
author: Robert Hartmann
author: Anne Henke
author: Steffen Koenig
author: Rowena Paget
published in: Mathematische Annalen
publication date: 2010-06-16T00:00:00Z
full work available at URL: cohstrat-final5a.pdf
review text: Combining the notions of cellular and stratified algebras the authors define a class of algebras which they call `cellularly stratified algebras'. In the definition the authors impose some extra conditions in addition to the cellular structure. These conditions strongly resemble properties of regular \(\mathcal D\)-classes in semigroups and ensure that the obtained algebra is also stratified in the sense of Cline, Parshall and Scott. The class of cellularly stratified algebras is shown to include many diagram algebras, in particular, Brauer algebras, Birman-Murakami-Wenzl algebras and partition algebras. The authors propose various structural characterizations for cellularly stratified algebras and study certain induction functors from layers of the stratification. The first application establishes tools for comparison of decomposition numbers for a cellularly stratified algebra and components of the stratification. The second application provides equivalences between certain categories of modules filtered by various structural modules. In the last section a Schur-Weyl duality for cellularly stratified algebras is presented.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16E35
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16W70
zbMATH DE Number: 5721504
zbMATH Keywords: cellularly stratified algebras
zbMATH Keywords: diagram algebras
zbMATH Keywords: stratifications
zbMATH Keywords: decomposition numbers
zbMATH Keywords: Schur-Weyl duality
zbMATH Keywords: exact functors
zbMATH Keywords: derived categories
zbMATH Keywords: equivalences of categories
MaRDI profile type: Publication
OpenAlex ID: W2017108713
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DOI: 10.1007/S00208-009-0458-X
description: scientific article; zbMATH DE number 5721504