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.

This page last modified by Alison Parker on Thu Jul 10 2003