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Opérades différentielles graduées sur les simplexes et les permutoèdres. (Differential graded operads related to simplices and permutohedra). (French) Zbl 1044.18007

The author defines several differential graded operads. These are related to families of polytopes. For the family \(\Pi\), the underlying complexes are cellular cochains of permutohedra, and for the family {Pasc} the underlying complexes are chains of standard simplices. Generators and relations presentations are given for these operads, for the operad \(K\) associated with associahedra [F. Chapoton, Trans. Am. Math. Soc. 354, 63–74 (2002; Zbl 1035.18006)], and for their duals. The matter in this paper completes nicely a diagram of operads that were introduced by J.-L. Loday [Lect. Notes Math. 1763, 7–66 (2001; Zbl 0999.17002)].

MSC:

18D50 Operads (MSC2010)
52B11 \(n\)-dimensional polytopes
17A32 Leibniz algebras
17D25 Lie-admissible algebras
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