Bounds on the global dimension of certain piecewise hereditary categories
arXiv:math/0607139 · doi:10.1016/j.jpaa.2007.12.007
Abstract
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.
7 pages; slightly revised; to appear in J. Pure Appl. Algebra