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arXiv · 2303.11513

Morphisms and extensions between bricks over preprojective algebras of type A

Eric J. Hanson·Xinrui You
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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.

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BibTeXRIS

Eric J. Hanson, Xinrui You. 2024-08-22. Morphisms and extensions between bricks over preprojective algebras of type A. https://doi.org/10.1016/j.jalgebra.2023.10.019

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