A. M. Semikhatov, “Factorizable ribbon quantum groups in logarithmic conformal field theories”, TMF, 154:3 (2008), 510–535; Theoret. and Math. Phys., 154:3 (2008), 433

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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 154, Number 3, Pages 510–535
DOI: https://doi.org/10.4213/tmf6184 (Mi tmf6184)

This article is cited in 16 scientific papers (total in 16 papers)

Factorizable ribbon quantum groups in logarithmic conformal field theories

A. M. Semikhatov

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Full-text PDF (802 kB) Citations (16)

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DOI: https://doi.org/10.4213/tmf6184

Abstract: We review the properties of quantum groups occurring as the 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.

Keywords: quantum group, factorizable structure, ribbon structure, modular group, Grothendieck ring, Kazhdan–Lusztig correspondence, logarithmic conformal field theory.

English version:
Theoretical and Mathematical Physics, 2008, Volume 154, Issue 3, Pages 433–453
DOI: https://doi.org/10.1007/s11232-008-0037-4

Bibliographic databases:

Language: Russian

Citation: A. M. Semikhatov, “Factorizable ribbon quantum groups in logarithmic conformal field theories”, TMF, 154:3 (2008), 510–535; Theoret. and Math. Phys., 154:3 (2008), 433–453

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Linking options:

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https://doi.org/10.4213/tmf6184

https://www.mathnet.ru/eng/tmf/v154/i3/p510

This publication is cited in the following 16 articles:

Semikhatov A.M., “Centralizing the Centralizers”, Lie Algebras, Vertex Operator Algebras, and Related Topics, Contemporary Mathematics, 695, ed. Barron K. Jurisich E. Milas A. Misra K., Amer Mathematical Soc, 2017, 239–259
Berenstein A., Greenstein J., “Generalized Joseph'S Decompositions”, C. R. Math., 353:10 (2015), 887–892
A. M. Semikhatov, “Fusion in the entwined category of Yetter–Drinfeld modules of a rank-1 Nichols algebra”, Theoret. and Math. Phys., 173:1 (2012), 1329–1358
Bushlanov P.V., Gainutdinov A.M., Tipunin I.Yu., “Kazhdan-Lusztig Equivalence and Fusion of Kac Modules in Virasoro Logarithmic Models”, Nucl. Phys. B, 862:1 (2012), 232–269
Semikhatov A.M. Tipunin I.Yu., “The Nichols Algebra of Screenings”, Commun. Contemp. Math., 14:4 (2012), 1250029
Semikhatov A.M., “Heisenberg Double H(B*) as a Braided Commutative Yetter-Drinfeld Module Algebra Over the Drinfeld Double”, Comm Algebra, 39:5 (2011), 1883–1906
Semikhatov A.M., “A Heisenberg double addition to the logarithmic Kazhdan-Lusztig duality”, Lett. Math. Phys., 92:1 (2010), 81–98
A. M. Semikhatov, “Quantum $s\ell(2)$ action on a divided-power quantum plane at even roots of unity”, Theoret. and Math. Phys., 164:1 (2010), 853–868
Fuchs J., Schweigert Ch., “Hopf algebras and finite tensor categories in conformal field theory”, Revista de La Union Matematica Argentina, 51:2 (2010), 43–90
G. S. Mutafyan, I. Yu. Tipunin, “Double affine Hecke algebra in logarithmic conformal field theory”, Funct Anal Its Appl, 44:1 (2010), 55
G. S. Mutafyan, I. Yu. Tipunin, “Double Affine Hecke Algebra in Logarithmic Conformal Field Theory”, Funct. Anal. Appl., 44:1 (2010), 55–64
A. M. Semikhatov, “A differential $\mathscr U$ -module algebra for $\mathscr{U}=\overline{\mathscr U}_{\mathfrak{q}}s\ell(2)$ at an even root of unity”, Theoret. and Math. Phys., 159:1 (2009), 424–447
A. M. Gainutdinov, “A generalization of the Verlinde formula in logarithmic conformal field theory”, Theoret. and Math. Phys., 159:2 (2009), 575–586
Bushlanov P.V., Feigin B.L., Gainutdinov A.M., Tipunin I.Yu., “Lusztig limit of quantum $\mathrm{sl}(2)$ at root of unity and fusion of $(1,p)$ Virasoro logarithmic minimal models”, Nuclear Phys. B, 818:3 (2009), 179–195
Adamović D., Milas A., “The $N=1$ triplet vertex operator superalgebras”, Comm. Math. Phys., 288:1 (2009), 225–270
Semikhatov A.M., “Higher string functions, higher-level Appell functions, and the logarithmic $\widehat{\mathrm{sl}}(2)_k/\mathrm{u}(1)$ CFT model”, Comm. Math. Phys., 286:2 (2009), 559–592

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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