Article Dans Une Revue Transactions of the American Mathematical Society Année : 2021

Operads with compatible CL-shellable partition posets admit a Poincaré-Birkhoff-Witt basis

Résumé

In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if and only if the associated partition posets are Cohen-Macaulay. Both notions of being Koszul and being Cohen-Macaulay admit different refinements: our goal here is to link two of these refinements. We more precisely prove that any (basic-set) operad whose associated posets admit isomorphism-compatible CL-shellings admits a Poincaré-Birkhoff-Witt basis. Furthermore, we give counterexamples to the converse.

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hal-01937173 , version 1 (27-11-2018)
hal-01937173 , version 2 (29-11-2022)
hal-01937173 , version 3 (12-06-2023)

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Joan Bellier-Millès, Bérénice Delcroix-Oger, Eric Hoffbeck. Operads with compatible CL-shellable partition posets admit a Poincaré-Birkhoff-Witt basis. Transactions of the American Mathematical Society, 2021, 374 (11), pp.8249-8273. ⟨10.1090/tran/8482⟩. ⟨hal-01937173v3⟩
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