An example of a quantum group: the twisted 𝑆𝑝_{𝑞}(2)

Paolucci, A.

doi:10.1090/S0002-9939-1994-1196167-8

An example of a quantum group: the twisted $\textrm {Sp}_ q(2)$
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Proc. Amer. Math. Soc. 122 (1994), 1-6 Request permission

Abstract:

We investigate the structure of the quantum symplectic group $\operatorname {Sp}(2)$ and give an explicit form for the fundamental representation. We prove that this group is a deformation of the classical compact group $\operatorname {Sp}(2)$ by showing that it is equivalent to the Reshetikhin, Takhtajan, Faddeev quantum $\operatorname {Sp}(2)$.

References

V. G. Drinfel′d, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. MR 934283
Michio Jimbo, Introduction to the Yang-Baxter equation, Braid group, knot theory and statistical mechanics, Adv. Ser. Math. Phys., vol. 9, World Sci. Publ., Teaneck, NJ, 1989, pp. 111–134. MR 1062425, DOI 10.1142/9789812798350_{0}005
S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613–665. MR 901157, DOI 10.1007/BF01219077
Shahn Majid, Quasitriangular Hopf algebras and Yang-Baxter equations, Internat. J. Modern Phys. A 5 (1990), no. 1, 1–91. MR 1027945, DOI 10.1142/S0217751X90000027
N. Yu. Reshetikhin, L. A. Takhtadzhyan, and L. D. Faddeev, Quantization of Lie groups and Lie algebras, Algebra i Analiz 1 (1989), no. 1, 178–206 (Russian); English transl., Leningrad Math. J. 1 (1990), no. 1, 193–225. MR 1015339
Jean-Michel Vallin, $C^\ast$-algèbres de Hopf et $C^\ast$-algèbres de Kac, Proc. London Math. Soc. (3) 50 (1985), no. 1, 131–174 (French). MR 765372, DOI 10.1112/plms/s3-50.1.131

Unitaires multiplicatifs et dualité pour les produits croisés de

algèbres

Victor Guillemin and Alan Pollack, Differential topology, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR 0348781
L. Faddeev, N. Reshetikhin, and L. Takhtajan, Quantum groups, Braid group, knot theory and statistical mechanics, Adv. Ser. Math. Phys., vol. 9, World Sci. Publ., Teaneck, NJ, 1989, pp. 97–110. MR 1062424, DOI 10.1142/9789812798350_{0}004
S. L. Woronowicz, Twisted $\textrm {SU}(2)$ group. An example of a noncommutative differential calculus, Publ. Res. Inst. Math. Sci. 23 (1987), no. 1, 117–181. MR 890482, DOI 10.2977/prims/1195176848