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Cohomological stratification of diagram algebras

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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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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany

    Robert Hartmann & Steffen Koenig

  2. Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford, OX1 3LB, UK

    Anne Henke

  3. School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK

    Rowena Paget

Authors
  1. Robert Hartmann
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  2. Anne Henke
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  3. Steffen Koenig
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  4. Rowena Paget
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Correspondence to Steffen Koenig.

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Hartmann, R., Henke, A., Koenig, S. et al. Cohomological stratification of diagram algebras. Math. Ann. 347, 765–804 (2010). https://doi.org/10.1007/s00208-009-0458-x

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