On representations of braid groups determined by directed graphs

We show that the two coproducts of a Markov $L$-coalgebra yield at least two solutions of the Yang-Baxter equation and thus at least two representations of braid groups

On some remarkable operads constructed from Baxter operators

Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this article is to study what type of (associative) algebras (and thus binary quadratic and non-symmetric operads) appear when such or such coalgebraic structures are used to decribe for instance combinatorial objects such as weighted directed graphs, trees, substitutions and so forth.Comment: 45 pages, 4 figure

Construction of Nijenhuis operators and dendriform trialgebras

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.Comment: 21 page