We give bounds on the global dimension of a finite length, piecewise hereditary category in terms of quantitative connectivity properties of its graph of indecomposables. We use this to show that the global dimension of a finite-dimensional, piecewise hereditary algebra A cannot exceed 3 if A is an incidence algebra of a finite poset or more generally, a sincere algebra. This bound is tight.
|Number of pages||6|
|Journal||Journal of Pure and Applied Algebra|
|State||Published - Sep 2008|
ASJC Scopus subject areas
- Algebra and Number Theory