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- W1496207212 abstract "On montre que la famille des modules de chaines des simplexes standards peut être munie d'une structure d'opérade. De même la famille des modules de cochaines des polytopes de Stasheff peut être munie d'une structure d'opérade. On montre que, d'une part, ces deux opérades sont duales l'une de l'autre, et, d'autre part, que ce sont des opérades de Koszul. Les algèbres sur l'opérade des simplexes standards, appellées trigèbres associatives, sont déterminées par 3 opérations et 11 relations. Les algèbres sur l'opérade des polytopes de Stasheff, appellées trigèbres dendriformes, sont déterminées par 3 opérations et 7 relations. We show that the family of chain modules over the standard simplices can be equipped with an operad structure. Similarly, the family of cochain modules of the Stasheff polytopes can be equipped with an operad structure. We first show that these operads are Koszul dual to each other, and second that they are both Koszul operads. The algebras over the standard simplices operad, called associative trialgebras, are defined by 3 operations and 11 relations. The algebras over the Stasheff polytopes operad, called dendriform trialgebras, are defined by 3 operations and 7 relations." @default.
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- W1496207212 date "2001-07-01" @default.
- W1496207212 modified "2023-09-25" @default.
- W1496207212 title "Une dualité entre simplexes standards et polytopes de Stasheff" @default.
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- W1496207212 doi "https://doi.org/10.1016/s0764-4442(01)02014-6" @default.
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