Morphisms and extensions between bricks over preprojective algebras of type A
arXiv:2303.11513 · doi:10.1016/j.jalgebra.2023.10.019
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.
v3: accepted manuscript. v2: additional references to related work, corrected an error in the proof of Proposition 6.6. 26 pages, 11 figures