23 citations · 32 across the 7 of their papers we have counts for
7 papers
A LL-lattice reformulation of arithmetree over planar rooted trees. Part II
Leroux Philippe
We continue our reformulation of free dendriform algebras, dealing this time with the free dendriform trialgebra generated be Y over planar rooted trees. We propose a 'deformation'…
Free dendriform dialgebras: reformulation and application in free probability. Part I
Leroux Philippe
We propose a reformulation of some results known on the free dendriform dialgebra on one generator from a parenthesis point of view. This turns out to be more tractable and point o…
On some remarkable operads constructed from Baxter operators
Leroux Philippe
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…
Construction of Nijenhuis operators and dendriform trialgebras
Leroux Philippe
Nijenhuis operators are constructed from particular bialgebras called dendriform- Nijenhuis bialgebras. It turns out that such operators commute with TD-operators, kind of Baxter-R…
From entangled codipterous coalgebras to coassociative manifolds
Leroux Philippe
We construct from coassociative coalgebras, bialgebras, Hopf algebras, new objects such as Poisson algebras, Leibniz algebras defined by J-L Loday and M. Ronco and explore the noti…
On representations of braid groups determined by directed graphs
Leroux Philippe
We show that the two coproducts of a Markov -coalgebra yield at least two solutions of the Yang-Baxter equation and thus at least two representations of braid groups.