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

Thomas Brüstle; Lutz Hille

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 2, page 295-303
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Brüstle, Thomas, and Hille, Lutz. "Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras." Colloquium Mathematicae 83.2 (2000): 295-303. <http://eudml.org/doc/210788>.

@article{Brüstle2000,
abstract = {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.},
author = {Brüstle, Thomas, Hille, Lutz},
journal = {Colloquium Mathematicae},
keywords = {categories of representations; quasi-hereditary algebras; orbits; Euler forms; directed algebras; exact categories; triangular matrix algebras; categories of prinjective modules; category equivalences},
language = {eng},
number = {2},
pages = {295-303},
title = {Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras},
url = {http://eudml.org/doc/210788},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Brüstle, Thomas
AU - Hille, Lutz
TI - Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 2
SP - 295
EP - 303
AB - 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.
LA - eng
KW - categories of representations; quasi-hereditary algebras; orbits; Euler forms; directed algebras; exact categories; triangular matrix algebras; categories of prinjective modules; category equivalences
UR - http://eudml.org/doc/210788
ER -

References

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