-exceptional sequences and the shard intersection order in type A

EJ Hanson - arXiv preprint arXiv:2303.11517, 2023 - arxiv.org
Reading's" shard intersection order" on the symmetric group can be realized as the" lattice of
wide subcategories" of the corresponding preprojective algebra. In this paper, we first use …

Maximal almost rigid modules over gentle algebras

E Barnard, RC Simoes, E Gunawan… - arXiv preprint arXiv …, 2024 - arxiv.org
We study maximal almost rigid modules over a gentle algebra $ A $. We prove that the
number of indecomposable direct summands of every maximal almost rigid $ A $-module is …

Triangulations of Prisms and Preprojective Algebras of Type A

O Iyama, NJ Williams - International Mathematics Research …, 2024 - academic.oup.com
We show that isomorphism classes of indecomposable-rigid pairs over, the preprojective
algebra of, are in bijection with internal-simplices in the prism, the product of an-simplex with …

Pop-Stack Operators for Torsion Classes and Cambrian Lattices

E Barnard, C Defant, EJ Hanson - arXiv preprint arXiv:2312.03959, 2023 - arxiv.org
The pop-stack operator of a finite lattice $ L $ is the map $\mathrm {pop}^{\downarrow}
_L\colon L\to L $ that sends each element $ x\in L $ to the meet of $\{x\}\cup\text {cov} _L (x) …