The Nichols algebra of screenings

Abstract

Two related constructions are associated with screening operators in models of two-dimensional conformal field theory. One is a local system constructed in terms of the braided vector space X spanned by the screening species in a given CFT model and the space of vertex operators Y and the other is the Nichols algebra B(X) and the category of its Yetter--Drinfeld modules, which we propose as an algebraic counterpart, in a "braided" version of the Kazhdan--Lusztig duality, of the representation category of vertex-operator algebras realized in logarithmic CFT models.