English

$\tau$-exceptional sequences for representations of quivers over local algebras

Representation Theory 2025-08-07 v2

Abstract

Let kk be an algebraically closed field. Let RR be a finite dimensional commutative local kk-algebra and let QQ be a quiver with no oriented cycles. In this paper, we study (signed) τ\tau-exceptional sequences over the algebra Λ=RkQ\Lambda = R\otimes kQ, which is isomorphic to RQRQ. We show there is a bijection between the set of complete (signed) τ\tau-exceptional sequences in mod kQ\text{mod }kQ and the set of complete (signed) τ\tau-exceptional sequences in mod Λ\text{mod }\Lambda. Moreover, we prove that every τ\tau-perpendicular subcategory of mod Λ\text{mod }\Lambda is equivalent to the module category of RkQR\otimes kQ', for some quiver QQ'. As a consequence, we prove that the τ\tau-cluster morphism categories of kQkQ and Λ\Lambda are equivalent.

Keywords

Cite

@article{arxiv.2502.15417,
  title  = {$\tau$-exceptional sequences for representations of quivers over local algebras},
  author = {Iacopo Nonis},
  journal= {arXiv preprint arXiv:2502.15417},
  year   = {2025}
}

Comments

39 pages. v2: Removed Proposition 5.2 and Corollary 5.12. Minor changes