Displaying similar documents to “On Lie algebras in braided categories”

About a family of naturally graded no p-filiform Lie algebras.

L. M. Camacho, J. R. Gómez, A. J. González (2005)

Extracta Mathematicae


The knowledge of the natural graded algebras of a given class of Lie algebras offers essential information about the structure of the class. So far, the classification of naturally graded Lie algebras is only known for some families of p-filiform Lie algebras. In certain sense, if g is a naturally graded Lie algebra of dimension n, the first case of no p-filiform Lie algebras it happens when the characteristic sequence is (n-3,2,1). We present the classification of a particular family...

From left modules to algebras over an operad: application to combinatorial Hopf algebras

Muriel Livernet (2010)

Annales mathématiques Blaise Pascal


The purpose of this paper is two fold: we study the behaviour of the forgetful functor from 𝕊 -modules to graded vector spaces in the context of algebras over an operad and derive the construction of combinatorial Hopf algebras. As a byproduct we obtain freeness and cofreeness results for those Hopf algebras. Let 𝒪 denote the forgetful functor from 𝕊 -modules to graded vector spaces. Left modules over an operad 𝒫 are treated as 𝒫 -algebras in the category of 𝕊 -modules. We generalize...

Local quasitriangular Hopf algebras.

Zhang, Shouchuan, Gould, Mark D., Zhang, Yao-Zhong (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]


Shuffle bialgebras

María Ronco (2011)

Annales de l’institut Fourier


The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive...