Bounds on the global dimension of certain piecewise hereditary categories

Details Bounds on the global dimension of certain piecewise hereditary categories Bounds on the global dimension of certain piecewise hereditary categories

2006-07-05

arxiv.org/abs/math/0607139v3

Journal of Pure and Applied Algebra 212 (2008), 2140-2145

Mathematics

Rings and Algebras

7 pages; slightly revised; to appear in J. Pure Appl. Algebra

Scientific paper

10.1016/j.jpaa.2007.12.007

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.

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