Enomoto's conjecture on infinite semibricks

Let AA be a finite-dimensional algebra over a field KK. A brick is a module MmodAM\in\operatorname{\mathsf{mod}} A whose endomorphism algebra EndA(M)\operatorname{\mathsf{End}}_A(M) is a division KK-algebra. An infinite semibrick is an infinite set of isoclasses of bricks that are pairwise Hom-orthogonal. The algebra AA is brick infinite if it has infinitely many isoclasses of bricks. Enomoto's conjecture. If AA is brick infinite, then there exists an infinite semibrick in modA\operatorname{\mathsf{mod}} A. The converse implication is immediate from the definitions, while the asserted existence of an infinite semibrick for every brick-infinite algebra is presented as an open conjecture; the paper notes that Enomoto gave a partial answer.

Sources & referencesView supporting material

Primary source

Sota Asai, “Bicompact torsion classes and conjectures on brick infinite algebras”, arXiv:2604.04505 (2026).

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