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arXiv · 2111.11376

Stratifying systems and $g$-vectors

Octavio Mendoza·Corina Sáenz·Hipolito Treffinger
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Abstract

In this paper we study the Cartan matrix associated to the Ext-projective stratifying system induced by a basic and $\tau$-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 $\tau$-rigid module can be calculated directly using these vectors. Moreover we characterise the stratifying systems coming from $\tau$-rigid modules that have a diagonal Cartan matrix.

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Octavio Mendoza, Corina Sáenz, Hipolito Treffinger. 2021-11-22. Stratifying systems and $g$-vectors. https://arxiv.org/abs/2111.11376

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