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

Lutz Hille ¹   ; Dieter Vossieck ²

¹ Mathematisches Seminar Universität Hamburg D-20146 Hamburg, Germany
² Am Frerks Hof 20 D-33647 Bielefeld, Germany

Colloquium Mathematicum, Tome 98 (2003) no. 2, pp. 201-211

Résumé

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.

Détail

DOI : 10.4064/cm98-2-6

Keywords: mit gamma finite dimensional hereditary basic algebra consider radical mathop rad nolimits mit gamma mit gamma bimodule known there exists quasi hereditary algebra mathcal category matrices mathop rad nolimits mit gamma equivalent category mit delta filtered mathcal modules mathcal mathcal mit delta note determine quasi hereditary algebra mathcal prove certain properties its module category