Abstract

In this paper we study the Cartan matrix associated to the Ext-projective stratifying system induced by a basic and τ -rigid object M in mod ( A ) by means of the g -vectors of the indecomposable direct summands of M . In particular we show that the Cartan group of a stratifying system associated to a τ -rigid module can be calculated directly using these vectors. Moreover we characterise the stratifying systems coming from τ -rigid modules that have a diagonal Cartan matrix.

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