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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Cited by in corpus (10)

• The N=1 triplet vertex operator superalgebras
• Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• The Nichols algebra of screenings
• Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• Heisenberg double H(B^*) as a braided commutative Yetter-Drinfeld module algebra over the Drinfeld double
• A Heisenberg double addition to the logarithmic Kazhdan--Lusztig duality
• A differential U-module algebra for U=U_q sl(2) at an even root of unity
• Generalized Joseph's decompositions
• Quantum-sl(2) action on a divided-power quantum plane at even roots of unity