Abstract
Multiparameter quantum gl(N) is not a rigid structure. This Letter defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of the parameters. All the equivalence classes of first-order essential deformations are found, as well as a class of exact deformations. This work provides quantization of all the classical Lie bialgebra structures (constantr-matrices) found by Belavin and Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a cubic root of unity, stands out.
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References
Belavin, A. A. and Drinfeld, V. G.,Soviet Sci. Rev. Math. 4, 93–165 (1984).
Drinfeld, V. G.,Quantum Groups, Intern. Congr. Math. Berkeley, 1986, pp. 798-820.
Jimbo, M.,Comm. Math. Phys. 102, 537–547 (1986).
Truini, P. and Varadarajan, V. S.,Lett. Math. Phys. 21, 287 (1991); Bonneau, P., Flato, M. and Pinczon, G.,Lett. Math. Phys. 25, 75-84 (1992).
Sudbery, A.,J. Phys. A 23, L967 (1990); Schirrmacher, A.,Z. Phys. C 50, 321 (1991); Reshetikhin, N. Y.,Lett. Math. Phys. 20, 331-336 (1990).
Woronowicz, L.,Publ. Res. Inst. Math. Sci. Kyoto Univ. 23, 117–181 (1987).
Reshetikhin, N. Y., ref. [5].
Fronsdal, C. and Galindo, A., New quantum groups, quantum planes and applications, Preprint UCLA/92/TEP/ and FT/UCM/4/92.
Fronsdal, C. and Galindo, A., The universalT-matrix,Proc. 1992 Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, Holyoke, June 1992, to be published (Preprint UCLA/93/TEP/2);Lett. Math. Phys. 27, 59-71 (1993).
Fronsdal, C., UniversalT-matrix for Twisted Quantum gl(N),Proc. NATO Workshop, San Antonio, February 1993.
Cremmer, E. and Gervais, J.-L.,Comm. Math. Phys. 134, 619–632 (1990).
Fronsdal, C., Cohomology and quantum groups,Proc. XXXth Karpacz Winter School of Theoretical Physics, February 1994, to be published.