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A duality between standard simplices and Stasheff polytopes

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arxiv math/0102089 v1 pith:FLXGMHW2 submitted 2001-02-12 math.QA math.ATmath.KT

Jean-Louis Loday , Maria O. Ronco This is my paper · ORCID
classification math.QAmath.ATmath.KT
keywords operadpolytopessimplicesstandardstasheffalgebrascalleddefined
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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.

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  1. Crossed modules of ternary Leibniz algebras

    math.RA 2025-01 reject novelty 4.0 of 10

    The paper transfers crossed modules from triassociative and Leibniz algebras to ternary Leibniz algebras, but omits the supporting computations and contains garbled formulas.

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