The finitistic dimension of algebras with a directed stratification]
Representation Theory
2011-02-15 v1
Abstract
We introduce the notion of a directed stratification for a finite-dimensional algebra. For algebras that admit such a stratification we characterise the projective resolutions of finitely generated modules and obtain a result for the finitistic dimension, which is an inductive version of a result of Fossum, Griffith and Reiten. With the developed techniques, which are adopted from the theory of EI-category algebras, we gain deeper insight in the combinatorial nature of this result. A characterisation of algebras which do not admit a directed stratification is given in terms of the Ext-quiver.
Keywords
Cite
@article{arxiv.1102.2577,
title = {The finitistic dimension of algebras with a directed stratification]},
author = {Karsten Dietrich},
journal= {arXiv preprint arXiv:1102.2577},
year = {2011}
}