Enomoto's conjecture on infinite semibricks
Enomoto's conjecture on infinite semibricks
Let be a finite-dimensional algebra over a field . A brick is a module whose endomorphism algebra is a division -algebra. An infinite semibrick is an infinite set of isoclasses of bricks that are pairwise Hom-orthogonal. The algebra is brick infinite if it has infinitely many isoclasses of bricks. Enomoto's conjecture. If is brick infinite, then there exists an infinite semibrick in . 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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