The semibrick conjecture

Let AA be an algebra, and call a set of pairwise Hom-orthogonal bricks in modA\operatorname{mod} A a semibrick. Call AA brick-infinite if it has infinitely many bricks up to isomorphism. Semibrick conjecture. Every brick-infinite algebra admits an infinite semibrick. The source states that this conjecture follows from the second brick-Brauer-Thrall conjecture and was originally motivated by extension-closed subcategories.

Sources & referencesView supporting material

Primary source

Kaveh Mousavand and Charles Paquette, “Hom-orthogonal modules and brick-Brauer-Thrall conjectures”, arXiv:2407.20877 (2025).

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