Factorizable ribbon quantum groups in logarithmic conformal field theories

Abstract

We review the properties of quantum groups occurring as Kazhdan--Lusztig dual to logarithmic conformal field theory models. These quantum groups at even roots of unity are not quasitriangular but are factorizable and have a ribbon structure; the modular group representation on their center coincides with the representation on generalized characters of the chiral algebra in logarithmic conformal field models.

27pp., amsart++, xy. v2: references added, some other minor additions

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