Cohomological stratification of diagram algebras

The class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras. While the definition is in combinatorial terms, by adding extra structure to Graham and Lehrer’s definition of cellular algebras, various structural properties are established in terms of e...

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Bibliographic Details
Published in:Mathematische annalen 2010-08, Vol.347 (4), p.765-804
Main Authors: Hartmann, Robert, Henke, Anne, Koenig, Steffen, Paget, Rowena
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:The class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras. While the definition is in combinatorial terms, by adding extra structure to Graham and Lehrer’s definition of cellular algebras, various structural properties are established in terms of exact functors and stratifications of derived categories. The stratifications relate ‘large’ algebras such as Brauer algebras to ‘smaller’ ones such as group algebras of symmetric groups. Among the applications are relative equivalences of categories extending those found by Hemmer and Nakano and by Hartmann and Paget, as well as identities between decomposition numbers and cohomology groups of ‘large’ and ‘small’ algebras.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-009-0458-x