The finitistic dimension of algebras with a directed stratification]

Details The finitistic dimension of algebras with a directed stratification] The finitistic dimension of algebras with a directed stratification]

2011-02-13

arxiv.org/abs/1102.2577v1

Mathematics

Representation Theory

Scientific paper

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.

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