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arXiv · 2401.07328

The non-decreasing condition on g-vectors

Mohamad Haerizadeh·Siamak Yassemi
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Abstract

The non-decreasing condition on g-vectors is introduced. Our study shows that this condition is both necessary and sufficient to ensure that the generically indecomposable direct summands of a given g-vector are linearly independent. Additionally, we prove that for any finite dimensional algebra $Λ$, under the non-decreasing condition, the number of generically indecomposable irreducible components that appear in the decomposition of a given generically $τ$-reduced component is lower than or equal to $|Λ|$. This solves the conjecture concerning the cardinality of component clusters by Cerulli-Labardini-Schröer, in a reasonable generality. Lastly, we study numerical criteria to check the wildness of g-vectors.

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BibTeXRIS

Mohamad Haerizadeh, Siamak Yassemi. 2025-01-29. The non-decreasing condition on g-vectors. https://doi.org/10.1016/j.jalgebra.2024.11.005

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