Abstract
We obtain Zakrzewski's deformation of Fun SL(2) through the construction of a *-product on SL(2). We then give the deformation of \((\mathfrak{s}\mathfrak{l}({\text{2}}))\) dual to this, as well as a Poincaré basis for both algebras.
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References
BergmanG. M., The diamond lemma for ring theory, Adv. in Math. 29, 178–218 (1978).
Deminov, E. E., Manin, Yu. I., Mukhin, E. E., and Zhdanovich, D. V., Nonstandard quantum deformations of GL(n) and constant solutions of the Yang-Baxter equation, preprint RIMS-701 (1990).
DrinfeldV. G., On constant, quasiclassical solutions of the Yang-Baxter quantum equation, Sov. Math. Dokl. 28, 667–671 (1983).
FaddeevL. D., ReshetikhinN. Yu., and TakhtajanL. A., Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1, 193–225 (1990).
ZakrzewskiS., A Hopf star-algebra of polynomials on the quantum SL(2, R) for a ‘unitary’ R-matrix, Lett. Math. Phys. 22, 287–289 (1991).
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Aspirant au Fonds National belge de la Recherche Scientifique. Partially supported by EEC contract SC1-0105-C.
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Ohn, C. A *-product on SL(2) and the corresponding nonstandard \((\mathfrak{s}\mathfrak{l}({\text{2}}))\) . Lett Math Phys 25, 85–88 (1992). https://doi.org/10.1007/BF00398304
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DOI: https://doi.org/10.1007/BF00398304