Morphisms and extensions between bricks over preprojective algebras of type A
Representation Theory
2024-08-23 v3
Abstract
The bricks over preprojective algebras of type A are known to be in bijection with certain combinatorial objects called "arcs". In this paper, we show how one can use arcs to compute bases for the Hom-spaces and first extension spaces between bricks. We then use this description to classify the "weak exceptional sequences" over these algebras. Finally, we explain how our result relates to a similar combinatorial model for the exceptional sequences over hereditary algebras of type A.
Cite
@article{arxiv.2303.11513,
title = {Morphisms and extensions between bricks over preprojective algebras of type A},
author = {Eric J. Hanson and Xinrui You},
journal= {arXiv preprint arXiv:2303.11513},
year = {2024}
}
Comments
v3: accepted manuscript. v2: additional references to related work, corrected an error in the proof of Proposition 6.6. 26 pages, 11 figures