45 citations · 52 across the 4 of their papers we have counts for
6 papers
The Hopf algebra of uniform block permutations. Extended abstract
Marcelo Aguiar, Rosa C. Orellana
We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permut…
The smash product of symmetric functions. Extended abstract
Marcelo Aguiar, Walter Ferrer, Walter Moreira
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tens…
Quadri-algebras
Marcelo Aguiar, Jean-Louis Loday
We introduce the notion of quadri-algebras. These are associative algebras for which the multiplication can be decomposed as the sum of four operations in a certain coherent manner…
Infinitesimal bialgebras, pre-Lie and dendriform algebras
Marcelo Aguiar
We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesima…
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations (Extended Abstract)
Marcelo Aguiar, Frank Sottile
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determ…
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations
Marcelo Aguiar, Frank Sottile
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determ…