Polarization and deformations of generalized dendriform algebras

Abstract

We generalize three results of M. Aguiar on Loday’s dendriform algebras to dendriform algebras associated with algebras satisfying any given set of relations. We adapt the concept of polarization to such algebras, and use it to generalize Aguiar’s results on deformations and filtrations of dendriform algebras. We introduce weak Rota–Baxter operators and use them to prove a generalization of another result by Aguiar, which provides an interpretation of the natural relation between infinitesimal bialgebras and pre-Lie algebras in terms of dendriform algebras.