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arXiv · 1811.11770

Operads with compatible CL-shellable partition posets admit a Poincar\'e-Birkhoff-Witt basis

Joan Bellier-Millès·Bérénice Delcroix-Oger·Eric Hoffbeck
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Abstract

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 Poincar\'e-Birkhoff-Witt basis. Furthermore, we give counter-examples to the converse.

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Joan Bellier-Millès, Bérénice Delcroix-Oger, Eric Hoffbeck. 2018-11-28. Operads with compatible CL-shellable partition posets admit a Poincar\'e-Birkhoff-Witt basis. https://arxiv.org/abs/1811.11770

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