International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 49-52, Pages 2595-2615
doi:10.1155/S0161171204402117
Construction of Nijenhuis operators and dendriform trialgebras
Philippe Leroux
Institut de Recherche Mathématique de Rennes, Université de Rennes I and CNRS UMR 6625, Campus de Beaulieu, Rennes Cedex 35042, France
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.