The Harish-Chandra theorem for the quantum algebra \(U_ q(sl(3))\). (English. Russian original) Zbl 0807.17011
Ukr. Math. J. 45, No. 3, 466-470 (1993); translation from Ukr. Mat. Zh. 45, No. 3, 436-439 (1993).
A basis of the quantum universal enveloping algebra \(U_ q (sl(3))\) is constructed to prove the Harish-Chandra theorem: For any nonzero element \(u\in U_ q (sl(3))\), there exists a finite-dimensional representation \(\pi\) such that \(\pi(u)=0\).
Reviewer: Ma Zhong-Qi (Beijing)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
References:
| [1] | Yu. A. Drozd, S. A. Ovsienko, and V. M. Futorny, ?On Gel’fand-Zetlin modules,?Suppl. Rend. Circolo Mat. Palermo, Ser. 2,26, 143-147 (1991). |
| [2] | V. G. Drinfel’d, ?Quantum groups,? in:Proceedings of the International Mathematical Congress, Vol.1, Academic Press, Berkeley, California (1986), pp. 798-820. |
| [3] | M. Jimbo, ?Aq-analogue ofU(gl (N+1)), Hecke Algebras, and the Yang-Baxter Equation,?Lett. Math. Phys.,11, 247-252 (1986). · Zbl 0602.17005 · doi:10.1007/BF00400222 |
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