Abstract
New solutions of Yang-Baxter equations including those associated with the fundamental representations of B n , C n and D n , Ř j 1/2 for V j ⊗ V 1/2 and colored R-matrix for SL q (2) with q a root of a unity are explicitly given. The related quantum group structures have been also set up. The Yang-Baxterization is performed to generate spectral parameter-depended solutions of YBE.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Yang-Baxter Equation in Integrable Systems, (M.Jimbo, ed.), World Scientific, Singapore, 1990. Pierre Cartier, Recent Development on The Applications of Braid Groups to Topology and Algebra, Seminare BOURBAKI, no 716 (November, 1989). L.C.Biedenharn, An Overview of Quantum Group, XVIIIthICGTMP, Moscow.
C.N. Yang, Phys.Rev.Lett. 19 (1967), 1312; Phys.Rev. 168 (1968), 1920.
Braid Group, Knot Theory and Statistical Mechanics (C.N.Yang and M.L.Ge, eds.), World Scientific, Singapore, 1989.
T. Kohno, in Knot Theory and Statistical Mechanics (C.N. Yang and M.L. Ge, eds.), World Scientific, Singapore, 1989, p. 135. L.D.Faddeev, Commun.Math.Phys 132 (1990), 131.
V.G. Drinfeld, Sov.Math.Dokl. 32 (1985), 254; Yang-Baxter Equation in Integrable Systems, (M.Jimbo ed.), World Scientific, Singapore, 1990.
M. Jimbo, Lett.Math.Phys. 10 (1985), 63.
M. Jimbo, Commun.Math.Phys. 102 (1986), 537.
N.Yu.Reshetikhin, Preprint LOMI E-4-87, 1988.
L.D.Faddeev, N.Yu.Reshetikhin and L.A. Takhtajan, Preprint LOMI E-14-87. L.A.Takhtajan, Nankai Lecture on Math.Phys.”Introduction to Quantum Group and Integrable Massive Models of Quantum Field Theory” (M.L.Ge and B.H.Zhao, eds.), World Scientific, 1990, pp. 69–197.
M. Wadati, T. Deguchi and Y. Akutsu, Phys.Reports. 180 (1989), 247. Braid Group, Knot Theory and Statistical Mechanics (C.N.Yang and M.L.Ge, eds.), World Scientific, Singapore, 1989, pp. 151–200.
H.J. de Vega, Adv.Studies in Pure Math. 19 (1989), 567; Inter.J.Mod.Phys. B4 (1990), 735.
A.A. Belavin and V.G. Drinfeld, Funct.Anal.Appl. 16 (1982), 159.
A.N. Kirillov and N.Yu. Reshetikhin, Commun. Math. Phys. 134 (1990), 421.
M.L. Ge,L.Y. Wang,Y.S. Wu and K. Xue, Inter.J.Mod.Phys. 4A (1989), 3351. M.L.Ge,Y.Q.Li and K.Xue, J.Phys. 23A (1990), 605; 619. M.L.Ge and K.Xue, Phys.Lett. 146A (1990), 245 152A (1990), 266.
M.L.Ge,Y.S.Wu and K.Hue, Explicit trigonometric Yang-Baxterization, ITP-SB-90-02; Inter.J.Mod.Phys. (to appear).
M.L. Ge and K. Hue, Proceedings of Workshop of Argonne National Laboratory (T. Curtright, D.B. Fairlie and C.K. Zachos, eds.), World Scientific, Singapore, 1990.
L.D. Faddeev,N.Yu. Reshetikhin and L.A. Takhtajan, Braid Group, Knot Theory and Statistical Mechanics (C.N. Yang and M.L. Ge, eds.), World Scientific, Singapore, 1989, p. 97.
H.C.Lee,M.Couture and N.C.Schmeing, CRNL-TP-1125R, Canada.
E.Cremmer and J.-L. Gervais, Preprint LPTENS 89/19, 1989.
M.Couture,Y.Cheng,M.L.Ge and K.Xue, Inter.J.Mod.Phys. 6A no 4. (1990).
V. Jones, Commun.Math.Phys. 125 (1989), 459.
Y. Cheng,M.L. Ge and K. Xue, Commun.Math.Phys. 136 (1990), 195; ITP-SB-90-38.
Y.Cheng,M.L.Ge and K.Xue, Construction of Non-standard Solutions for YBE in Terms-of q-Deformed Boson Representations of SL q (2) with q a Root of Unity, Nankai preprint, 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag
About this paper
Cite this paper
Ge, ML. (1992). New solutions of Yang-Baxter equations and quantum group structures. In: Kulish, P.P. (eds) Quantum Groups. Lecture Notes in Mathematics, vol 1510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101193
Download citation
DOI: https://doi.org/10.1007/BFb0101193
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55305-2
Online ISBN: 978-3-540-47020-5
eBook Packages: Springer Book Archive