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Algebras and Representation Theory

, Volume 6, Issue 1, pp 97–117 | Cite as

Quasi-Hereditary Extension Algebras

  • István Ágoston
  • Vlastimil Dlab
  • Erzsébet Lukács
Article

Abstract

The paper is a continuation of the authors' study of quasi-hereditary algebras whose Yoneda extension algebras (homological duals) are quasi-hereditary. The so-called standard Koszul quasi-hereditary algebras, presented in this paper, have the property that their extension algebras are always quasi-hereditary. In the natural setting of graded Koszul algebras, the converse also holds: if the extension algebra of a graded Koszul quasi-hereditary algebra is quasi-hereditary, then the algebra must be standard Koszul. This implies that the class of graded standard Koszul quasi-hereditary algebras is closed with respect to homological duality. Another immediate consequence is the fact that all algebras corresponding to the blocks of the category O are standard Koszul.

quasi-hereditary algebra Yoneda extension algebra Koszul algebra Bernstein–Gelfand–Gelfand category O 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • István Ágoston
    • 1
  • Vlastimil Dlab
    • 2
  • Erzsébet Lukács
    • 3
  1. 1.Department of Algebra and Number TheoryEötvös UniversityBudapestHungary
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  3. 3.Department of AlgebraTechnical University of BudapestBudapestHungary

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