Intersection vectors over skew-tilings

2025/11/16 by Deng, Difan, Geng, Shengfei, Liu, Pin
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.12619

Abstract

We prove that under a mild condition, a multiset of tagged permissible arcs over a skew-tiling is uniquely determined by its intersection vector. As an application, it is proved that -- up to isomorphism -- different τ-rigid modules over a skew-gentle algebra A arising from a skew-triple (Q,Sp,I) have different dimension vectors if and only if (Q,I) has no minimal oriented cycle of even-length with full zero relations. This generalizes a recent work of Fu-Geng for gentle algebras.

Citations

• Intersection vectors over tilings with applications to gentle algebras and cluster algebras
• A geometric model for the module category of a skew-gentle algebra
• A geometric model for the module category of a gentle algebra
• Gentle algebras arising from surface triangulations
• q-Cartan matrices and combinatorial invariants of derived categories for skewed-gentle algebras
• Tilting theory and cluster combinatorics
• Cluster algebras I: Foundations

Related

• Intersection vectors over tilings with applications to gentle algebras and cluster algebras
• A geometric model for the module category of a skew-gentle algebra
• Two geometric models for graded skew-gentle algebras
• A geometric model for the non-τ-rigid modules of type \widetildeD_n
• Dimension vectors of τ-rigid modules and f-vectors of cluster monomials from triangulated surfaces