Cohomological stratification of diagram algebras |
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Authors: | Robert Hartmann Anne Henke Steffen Koenig Rowena Paget |
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Institution: | (1) Department of Mathematics, East China Normal University, Shanghai, 200062, China |
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Abstract: | 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. |
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