Abstract
A basis of a quantum universal enveloping algebraU is constructed; the following theorem is proved with the help of this basis: For any nonzero element Μ ∃U, there exists a finite-dimensional representation π such thatπ(u) ≠ 0.
References
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).
V. G. Drinfel'd, “Quantum groups,” in:Proceedings of the International Mathematical Congress, Vol.1, Academic Press, Berkeley, California (1986), pp. 798–820.
M. Jimbo, “Aq-analogue ofU(gl (N+1)), Hecke Algebras, and the Yang-Baxter Equation,”Lett. Math. Phys.,11, 247–252 (1986).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45 No. 3, pp. 436–439, March, 1993.
Rights and permissions
About this article
Cite this article
Guzner, B.Z. The Harish-Chandra theorem for the quantum algebrau q (sl (3)). Ukr Math J 45, 466–470 (1993). https://doi.org/10.1007/BF01061020
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01061020