Bounds on the global dimension of certain piecewise hereditary categories
Rings and Algebras
2008-05-26 v3 Representation Theory
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.
Keywords
Cite
@article{arxiv.math/0607139,
title = {Bounds on the global dimension of certain piecewise hereditary categories},
author = {Sefi Ladkani},
journal= {arXiv preprint arXiv:math/0607139},
year = {2008}
}
Comments
7 pages; slightly revised; to appear in J. Pure Appl. Algebra