The Nichols algebra of screenings (Q2909792)

This paper deals with the discussion of how representation categories of braided Hopf algebras can be associated with nonsemisimple (logarithmic) models of conformal field theory (briefly CFT). The authors' proposal is about considering the problem from another perspective. They suggest to take the algebra of screening operators, regarded as a braided Hopf algebra, and construct a category of Yetter-Drinfeld modules from other CFT data, the vertex operators in a given model. Screening operators generate Nichols algebras. Indeed, the authors use screened vertex operators to construct the categories of Hopf bimodules and Yetter-Drinfeld modules over Nichols algebras of screenings. By doing this they propose as an algebraic counterpart, in a ``braided'' version of the Kazhdan-Lusztig duality, the representation category of vertex-operator algebras realized in logarithmic CFT models.