On the string Lie algebra

2014/07/25 by Salim Riviere, Riviere, Salim, Friedrich Wagemann +1
Mathematics · Physics and Astronomy · #17B56 #FOS: Mathematics #FOS: Physical sciences #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.KT #math.MP #math.QA #msc:17B56

paper · pdf · doi:10.48550/arxiv.1407.6806

29 pages

arxiv created 2014/07/25 · arxiv updated 2014/07/28

Abstract

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.

Related

• Braided modules and reflection equations
• Bicharacters, braids and Jacobi identity
• Braiding for categorical algebras and crossed modules of algebras II:\n Leibniz algebras
• Categorification of infinite-dimensional \mathfraksl₂-modules and braid group 2-actions I: tensor products
• Representations of crossed modules and other generalized Yetter-Drinfel'd modules