The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Volume 98 / 2003
Colloquium Mathematicum 98 (2003), 201-211
MSC: 14L30, 16E99, 22E47.
DOI: 10.4064/cm98-2-6
Abstract
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.
