Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras
Colloquium Mathematicum, Tome 83 (2000) no. 2, pp. 295-303
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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.
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author = {Thomas Br\"ustle and Lutz Hille},
title = {Matrices over upper triangular bimodules and {\ensuremath{\Delta}-filtered} modules over quasi-hereditary algebras},
journal = {Colloquium Mathematicum},
pages = {295--303},
publisher = {mathdoc},
volume = {83},
number = {2},
year = {2000},
doi = {10.4064/cm-83-2-295-303},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-83-2-295-303/}
}
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Thomas Brüstle; Lutz Hille. Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras. Colloquium Mathematicum, Tome 83 (2000) no. 2, pp. 295-303. doi: 10.4064/cm-83-2-295-303
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