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.
Domaines
Topologie algébrique [math.AT]
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