725 research outputs found
On representations of braid groups determined by directed graphs
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
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
From entangled codipterous coalgebras to coassociative manifolds
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 notion of coassociative manifolds.Comment: 25 pages, 13 figure
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