The Harish-Chandra theorem for the quantum algebra $u_q (\text{sl} (3))$ - Guzner, B. Z. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
A basis of a quantum universal enveloping algebra $U$ 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 that $π(u) ≠ 0$.