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Bounds on the global dimension of certain piecewise hereditary categories

Sefi Ladkani
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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.

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Sefi Ladkani. 2008-01-03. Bounds on the global dimension of certain piecewise hereditary categories. https://doi.org/10.1016/j.jpaa.2007.12.007

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