Abstract. We first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL2 and SL3. We use these to show that the global dimension of a Schur algebra for GL2 and GL3 is twice the good filtration dimension. To do this for SL3, we give an explicit filtration of the modul...

Let k be an algebraically closed field. The generalized or n-Kronecker quiver K(n) is the with two vertices, called a source and sink, n arrows from to sink. Given finite-dimensional module M of path algebra kK(n)=Kn, we consider its dimension vector dim¯M=(dimkM1,dimkM2). F={(x,y)|2nx≤y≤x}, let (x,y)∈F. We construct X(x, y) Kn, prove it elementary. Suppose that dim¯M=(x,y). show that:if elemen...

We prove rigidity type results on the vanishing of stable Ext and Tor for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of prerigidity, which generalizes phenomena for modules of finite complete intersection dimension and complexity one. Using this concept, we prove results on length and vanishing of homolo...