A geometrically motivated investigation of the Tor-groups of quasi- hereditary algebras (Q2644742)

Let A be a quasi-hereditary algebra and let \(e\in A\) be an idempotent such that \(J=AeA\) is an ideal occuring in the definition of a heredity chain of A (see \textit{V. Dlab} and \textit{C. M. Ringel} [Ill. J. Math. 33, 280-291 (1989; Zbl 0666.16014)]). It is shown in the paper that the functor A/J\(\otimes (\)-): mod(A)\(\to mod(A/J)\) is exact on the full subcategory of mod(A) of finitely generated left A-modules having a Weyl filtration with respect to a given heredity chain of A, whereas the functor \(Ae\otimes_{eAe}(\)-): mod(eAe)\(\to mod(A)\) is exact on the category of left eAe-modules having a Weyl filtration with respect to the induced heredity chain of eAe. Some applications of these facts are given.