Factorisation quantum groups

Abstract: We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex algebra case this generalises previous notions due to Etingof-Kazhdan and Frenkel-Reshetikhin. Finally we give examples, including Borcherds twists and homology vertex algebras.