Bounds on the global dimension of certain piecewise hereditary categories

Sefi Ladkani

doi:10.1016/j.jpaa.2007.12.007

Bounds on the global dimension of certain piecewise hereditary categories

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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.

Original language	English
Pages (from-to)	2140-2145
Number of pages	6
Journal	Journal of Pure and Applied Algebra
Volume	212
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2007.12.007
State	Published - Sep 2008
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2007.12.007

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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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Bounds on the global dimension of certain piecewise hereditary categories

Abstract

ASJC Scopus subject areas

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