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Mathematische Annalen

, Volume 347, Issue 4, pp 765–804 | Cite as

Cohomological stratification of diagram algebras

  • Robert Hartmann
  • Anne Henke
  • Steffen KoenigEmail author
  • Rowena Paget
Article

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.

Keywords

Symmetric Group Direct Summand Cell Module Young Module Specht Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Robert Hartmann
    • 1
  • Anne Henke
    • 2
  • Steffen Koenig
    • 1
    Email author
  • Rowena Paget
    • 3
  1. 1.Mathematisches InstitutUniversität zu KölnKölnGermany
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK
  3. 3.School of Mathematics, Statistics and Actuarial ScienceUniversity of KentCanterburyUK

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