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• W3092864583 abstract "Let $$Lambda $$ be a finite-dimensional associative algebra over a field. A semibrick pair is a finite set of $$Lambda $$ -modules for which certain Hom- and Ext-sets vanish. A semibrick pair is completable if it can be enlarged so that a generating condition is satisfied. We prove that if $$Lambda $$ is $$tau $$ -tilting finite with at most three simple modules, then the completability of a semibrick pair can be characterized using conditions on pairs of modules. We then use the weak order to construct a combinatorial model for the semibrick pairs of preprojective algebras of type $$A_n$$ . From this model, we deduce that any semibrick pair of size n satisfies the generating condition, and that the dimension vectors of any semibrick pair form a subset of the column vectors of some c-matrix. Finally, we show that no “pairwise” criteria for completability exists for preprojective algebras of Dynkin diagrams with more than three vertices." @default.
• W3092864583 created "2020-10-22" @default.
• W3092864583 creator A5038510773 @default.
• W3092864583 creator A5059668597 @default.
• W3092864583 date "2022-05-16" @default.
• W3092864583 modified "2023-10-05" @default.
• W3092864583 title "Pairwise Compatibility for 2-Simple Minded Collections II: Preprojective Algebras and Semibrick Pairs of Full Rank" @default.
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• W3092864583 doi "https://doi.org/10.1007/s00026-022-00585-4" @default.
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