Operads with compatible CL-shellable partition posets admit a Poincaré-Birkhoff-Witt basis
نویسندگان
چکیده
In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if only the associated partition are Cohen-Macaulay. Both notions of being CohenâMacaulay admit different refinements: our goal here to link two these refinements. We more precisely prove any (basic-set) whose isomorphism-compatible CL-shellings admits PoincaréâBirkhoffâWitt basis. Furthermore, we give counter-examples converse.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2021
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8482