Construction of Nijenhuis operators and dendriform trialgebras

2003/11/09 by Leroux Philippe, Philippe, Leroux
Mathematics · Physics and Astronomy · #17A30 #18D50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:17A30 #msc:18D50

paper · pdf · doi:10.48550/arxiv.math/0311132

21 pages

arxiv created 2003/11/09 · arxiv updated 2009/12/01

Abstract

Nijenhuis operators are constructed from particular bialgebras called dendriform- Nijenhuis bialgebras. It turns out that such operators commute with TD-operators, kind of Baxter-Rota operators, and therefore closely related to dendriform trialgebras. Examples are given.

Related

• Rota-type operators on 2-dimensional dendriform algebras
• Quasi-triangular and factorizable dendriform D-bialgebras
• Generalized NS-algebras
• Quasi-triangular, factorizable anti-dendriform bialgebras and relative Rota-Baxter operators
• Leibniz-dendriform bialgebras and relative Rota-Baxter operators