Abstract
We construct universal twists connecting the centrally extended double Yangian DYrm(sl(2))c with deformed double Yangians DYrm(sl(2))c, thereby establishing the quasi-Hopf structures of the latter.
Similar content being viewed by others
References
Babelon, O.: Universal exchange algebra for Bloch waves and Liouville theory, Comm. Math. Phys. 139 (1991), 619.
Arnaudon, D., Buffenoir, E., Ragoucy, E. and Roche, Ph.: Universal solutions of quantum dynamical Yang-Baxter equations, Lett. Math. Phys. 44 (1998), 201; q-alg/9712037.
Jimbo, M., Konno, H., Odake, S. and Shiraishi, J.: Quasi-Hopf twistors for elliptic quantum groups, 'Transformation groups' and q-alg/9712029.
Konno, H.: Degeneration of the elliptic algebra \({\mathcal{A}}_{q,p} (\widehat{sl}(2))\) and form factors in the Sine-Gordon theory, Proc. Nankai-CRM Joint Meeting on 'Extended and Quantum Algebras and their Applications to Physics', Tianjin, China, 1996; hep-th/9701034.
Jimbo, M., Konno, H. and Miwa, T.: Massless XXZ model and degeneration of the elliptic algebra \({\mathcal{A}}_{q,p} (\widehat{sl}(2))\), In: Ascona 1996, 'Deformation Theory and Symplectic Geometry', pp. 117–138 and hep-th/9610079.
Khoroshkin, S., Lebedev, D. and Pakuliak, S.: Elliptic algebra \({\mathcal{A}}_{q,p} (\widehat{sl_2 })\) in the scaling limit, Comm. Math. Phys. 190 (1998), 597; q-alg/9702002.
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E. and Rossi, M.: Cladistics of double Yangian and elliptic algebras, Preprint LAPTH-738/99, PAR-LPTHE 99-236 and DTP-99-45, math.QA/9906189.
Bernard, D. and LeClair, A.: The quantum double in integrable quantum field theory, Nuclear Phys. B 399 (1993), 709.
Khoroshkin, S.M. and Tolstoy, V.N.: Yangian double and rational R matrix, Lett. Math. Phys. (1995), and hep-th/9406194.
Faddeev, L. D., Reshetikhin, N. Yu. and Takhtajan, L. A.: Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1 (1990), 193.
Khoroshkin, S. M.: Central extension of the Yangian double, Collection SMF, 7ème rencontre du contact franco-belge en algèbre, Reims 1995, q-alg/9602031.
Buffenoir, E. and Roche, Ph.: Harmonic analysis on the quantum Lorentz group, Comm. Math. Phys. 207 (1999), 499–555; q-alg/9710022.
Barnes, E. W.: The theory of the double gamma function, Philos. Trans. Roy. Soc. A 196 (1901), 265–388.
Jimbo, M. and Miwa, T.: q = 1 and correlation functions of the XXZ model in the gapless regime, J. Phys. A (Math. Gen.) 29 (1996), 2923; hep-th/9601135.
Etingof, P., Schedler T. and Schiffmann, O.: Explicit quantization of dynamical r-matrices for finite dimensional semisimple Lie algebras; math.QA/9912009.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Arnaudon, D., Avan, J., Frappat, L. et al. On the Quasi-Hopf Structure of Deformed Double Yangians. Letters in Mathematical Physics 51, 193–204 (2000). https://doi.org/10.1023/A:1007680606524
Issue Date:
DOI: https://doi.org/10.1023/A:1007680606524