On the string Lie algebra

Salim Riviere (1) , Friedrich Wagemann (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We construct an abelian representative for the crossed module associated to the string Lie algebra. We show how to apply this construction in order to define quasi-invariant tensors which serve to categorify the infinitesimal braiding on the category of g-modules given by an r-matrix, following Cirio-Martins.

Domaines: Algèbres quantiques [math.QA]; K-théorie et homologie [math.KT]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Salim Riviere, Friedrich Wagemann. On the string Lie algebra. Algebras and Representation Theory, 2015, 18 (4), pp.1071-1099. ⟨hal-01057781⟩