Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras

Volume 83 / 2000

Thomas Brüstle, Lutz Hille Colloquium Mathematicum 83 (2000), 295-303 DOI: 10.4064/cm-83-2-295-303


Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent to mat B is Morita equivalent to A.


  • Thomas Brüstle
  • Lutz Hille

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