$\tau$-exceptional sequences for representations of quivers over local algebras
Representation Theory
2025-08-07 v2
Abstract
Let be an algebraically closed field. Let be a finite dimensional commutative local -algebra and let be a quiver with no oriented cycles. In this paper, we study (signed) -exceptional sequences over the algebra , which is isomorphic to . We show there is a bijection between the set of complete (signed) -exceptional sequences in and the set of complete (signed) -exceptional sequences in . Moreover, we prove that every -perpendicular subcategory of is equivalent to the module category of , for some quiver . As a consequence, we prove that the -cluster morphism categories of and 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