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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.13578 |
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Table of Contents:
- We extend the notion of stability in the non-abelian category of poset representations (introduced by Futorny and Iusenko) to the category of socle-projective representations of a given $r$-peak poset $¶$. When $¶$ is a poset of type $\mathbb{A}$, we demonstrate in two distinct ways that every indecomposable peak $¶$-space is stable. First, this is shown using a bilinear form associated with the poset. Second, we prove it by observing that a stability function derived from a geometric model ensures that all indecomposable objects are stable. Along the way, we provide a new geometric realization of the category of socle-projective representations, inspired by the work of Schiffler and Serna [\textit{J. Pure Appl. Algebra} \textbf{224} (2020), no.~12, 106436, 23 pp.; MR4101480]. Finally, we establish a connection between the geometric perspective and the bilinear form approach.