The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra

Volume 98 / 2003

Lutz Hille, Dieter Vossieck Colloquium Mathematicum 98 (2003), 201-211 MSC: 14L30, 16E99, 22E47. DOI: 10.4064/cm98-2-6


Let ${\mit \Gamma }$ be a finite-dimensional hereditary basic algebra. We consider the radical $\mathop {\rm rad}\nolimits {\mit \Gamma }$ as a ${\mit \Gamma }$-bimodule. It is known that there exists a quasi-hereditary algebra ${\mathcal {A}}$ such that the category of matrices over $\mathop {\rm rad}\nolimits {\mit \Gamma }$ is equivalent to the category of ${\mit \Delta }$-filtered ${\mathcal {A}}$-modules ${\mathcal {F}}({\mathcal {A}},{\mit \Delta })$. In this note we determine the quasi-hereditary algebra ${\mathcal {A}}$ and prove certain properties of its module category.


  • Lutz HilleMathematisches Seminar
    Universität Hamburg
    D-20146 Hamburg, Germany
  • Dieter VossieckAm Frerks Hof 20
    D-33647 Bielefeld, Germany

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