The semibrick-pair completion conjecture for tau-tilting finite algebras
The semibrick-pair completion conjecture for tau-tilting finite algebras
Let be a -tilting finite algebra, and let be a semibrick pair, meaning a collection of bricks in the indicated degrees satisfying the relevant hom-orthogonality conditions. Let the smallest wide subcategory containing be the wide subcategory generated by this pair. Semibrick-pair completion conjecture. The pair is completable if and only if the smallest wide subcategory containing it has simple objects. This concerns when semibrick pairs extend to 2-term simple minded collections in the -tilting finite setting; the supplied text does not state whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Emily Barnard and Eric J. Hanson, “Pairwise Compatibility for 2-Simple Minded Collections II: Preprojective Algebras and Semibrick Pairs of Full Rank”, arXiv:2010.08645 (2023).
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