Yangians as Pre-Lie and Tridendriform Algebras

Based on the rigorous discrete derivations of Dyson series and the Magnus expansion, key links between quantum algebras, tridendriform and pre-Lie algebras are established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras actions.