Tiling the (n^2,1)-De Bruijn graph with n coassociative coalgebras

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.

Analytic subordination results in free probability from non-coassociative derivation-comultiplications

We extend Voiculescu's approach to analytic subordination through the coalgebra of the free difference quotient to non-coassociative derivation-comultiplications appearing in free probability theory. We obtain new proofs of Voiculescu's analytic subordination results for freely Markovian triples, and for multiplication of unitaries which are free with amalgamation.

Coalgebras of words and phrases

We introduce two constructions of a coassociative comultiplication in the algebra of phrases in a given alphabet. As a preliminary step we give two constructions of a pre-Lie comultiplication in the module generated by words.

Coassociativity breaking and oriented graphs

This paper is an attempt to unify coassociative coalgebra theory and random walks on oriented graphs.

单色余代数的结构

The structure of simply colored coalgebras

本文研究单色余代数的结构，证明了域上单色余代数与带余根分裂选择的点余代数等价，并证明其范畴完备且余完备。