Etude de l'algèbre de Lie double des arbres enracinés décorés

Loïc Foissy (1)

1 LMR - Laboratoire de Mathématiques de Reims

the double Lie algebra L^D of rooted trees decorated by a set D is introduced, generalising the construction of Connes and Kreimer. It is shown that it is a simple Lie algebra. Its derivations and its automorphisms are described, as well as some central extensions. Finally, the category of lowest weight modules is introduced and studied.

Mots clés: Lie algebra; rooted trees; lowest weight modules

Domaines: Anneaux et algèbres [math.RA]

Loïc Foissy. Etude de l'algèbre de Lie double des arbres enracinés décorés. Advances in Mathematics, 2007. ⟨hal-00160832⟩