Paper Abstract

Title

On the global and good filtration dimensions of quasi-hereditary algebras

Abstract

In this paper we consider how the good, Weyl and global dimensions of a quasi-hereditary algebra are interrelated. We first consider how these dimensions are affected by the Ringel dual and by two forms of truncation. We then restrict our attention to quasi-hereditary algebras with simple preserving duality. We consider various orders on the poset compatible with quasi-hereditary structure and the good, Weyl and injective dimensions of the simple and the costandard modules. Finally we take a strong version of one of these properties (namely that if $\mu < \lambda$ then $\gfd(L(\mu)) < \gfd(L(\lambda))$ where $\mu, \lambda$ are in the poset and $L(\mu)$, $L(\lambda)$ are the corresponding simples) and show that in this case the global dimension of the algebra is twice its good filtration dimension.