Bounds on the global dimension of certain piecewise hereditary categories

• Autores: Sefi Ladkani
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 9, 2008, págs. 2140-2145
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.12.007
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• Resumen

  • 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.