Stratifying systems and g-vectors

Stratifying systems and g-vectors

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-r...

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Veröffentlicht in:Journal of pure and applied algebra 2023-03, Vol.227 (3), p.107212, Article 107212
Hauptverfasser: Mendoza, Octavio, Sáenz, Corina, Treffinger, Hipolito
Format: Artikel
Sprache:eng
Schlagworte:
Cartan matrices and groups
g-vectors
Mathematics
Representation Theory
Stratifying systems
Weakly triangular algebras
τ-rigid modules
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Zusammenfassung: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.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2022.107212