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Construction of Nijenhuis operators and dendriform trialgebras

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  • Philippe Leroux

Abstract

We construct Nijenhuis operators from particular bialgebras called dendriform-Nijenhuis bialgebras. It turns out that such Nijenhuis operators commute with TD -operators, a kind of Baxter-Rota operators, and are therefore closely related to dendriform trialgebras. This allows the construction of associative algebras, called dendriform-Nijenhuis algebras, made out of nine operations and presenting an exotic combinatorial property. We also show that the augmented free dendriform-Nijenhuis algebra and its commutative version have a structure of connected Hopf algebras. Examples are given.

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  • Philippe Leroux, 2004. "Construction of Nijenhuis operators and dendriform trialgebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-21, January.
    • Handle: RePEc:hin:jijmms:965786
    DOI: 10.1155/S0161171204402117
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