Factorizable ribbon quantum groups in logarithmic conformal field theories

2007/05/31 by AM Semikhatov, A. M. Semikhatov
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #hep-th #math.QA

paper · pdf · doi:10.1007/s11232-008-0037-4

published as Theor.Math.Phys.154:433-453,2008 · 27pp., amsart++, xy. v2: references added, some other minor additions

arxiv created 2007/06/19 · openalex publication_date 2008/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

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.

Citations

• On Verlinde-Like Formulas in c_p,1 Logarithmic Conformal Field Theories
• Symmetric linear functions of the restricted quantum group U_qsl₂(ℂ)
• The small quantum group and the Springer resolution
• Quantum R-matrices and factorization problems