Construction of Nijenhuis operators and dendriform trialgebras

Philippe Leroux

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-21

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:965786

DOI: 10.1155/S0161171204402117

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