Abstract
Existing definition of a real form of quantum group as a *-Hopf algebra is not quite satisfactory from the categorical point of view. In this paper another definition is proposed, which essentially coincides with the previous one for q∈ℝ and yields new examples for |q|=1. The last case is important because of applications of quantum groups to conformal field theory.
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References
Deligne P., Milne J.S., Tannakian Categories, Lect. Notes Math. 900 (1982), 101–228, Springer, Berlin a.o..
Drinfeld, V.G., Quantum groups, Proc. of the ICM-86 1 (1987), 798–820, Berkeley.
Goto, M., Grosshans, F.D., Semisimple Lie algebras, Lect.Notes Pure Appl.Math. 38 (1978), Marsel Dekker, N.Y. and Basel.
Jimbo, M., A q-Difference Analogue of U q (g) and the Yang-Baxter Equation, Lett.Math.Phys. 10 (1985), 63–69.
Khoroshkin, S.M., Tolstoy, V.N., Universal R-matrix for quantum supergroups (to appear).
Kirillov, A.N., Reshetikhin, N.Yu., q-Weyl Group and a Multiplicative Formula for Universal R-matrices, Commun. Math. Phys. 134 (1991), 421–431.
Levendorskii, S., Soibelman, Ya., Some applications of the quantum Weyl group, Preprint (1989).
Lusztig, G., Finite dimensional Hopf algebras arising from quantum groups, Preprint.
Lyubashenko, V.V., Tensor categroies and RCFT. I. Hopf algebras in rigid categories, Preprint no. ITP-90-30E (1990), Kiev; Tensor categories and RCFT. II. Modular transformations, Preprint no. ITP-90-59E (1990), Kiev.
Majid S., Duals and Doubles of Monoidal Categories, Preprint no. DAMTP/89-41 (1989).
Reshetikhin, N.Yu., Quasitriangular Hopf algebras, solutions of the Yang-Baxter equation and invariants of links, Algebra Anal 1 no. 2 (1989), 169–194. (in Russian)
Saavedra, R.N., Catégories Tannakiennes, Lect. Notes Math. 265 (1972), 420, Springer, Heidelberg.
Soibelman, Ya.S., Quantum Weyl group and some of its applications, Supl.Rend.Circ.Mat.Palermo (1990), (to appear).
Turaev, V.G., Operator invariants of links and R-matrices, Izv.Akad.Nauk SSSR, Ser.Mat. 53 no. 5 (1989), 1073–1107. (in Russian)
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© 1992 Springer-Verlag
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Lyubashenko, V. (1992). Real and imaginary forms of quantum groups. In: Kulish, P.P. (eds) Quantum Groups. Lecture Notes in Mathematics, vol 1510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101179
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DOI: https://doi.org/10.1007/BFb0101179
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