Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras
Tom 83 / 2000
Colloquium Mathematicum 83 (2000), 295-303
DOI: 10.4064/cm-83-2-295-303
Streszczenie
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.
