Quantized enveloping algebras


(from Jantzen: Quantum Groups)

(R2) means:
    the q(α,β)-commutator
    of Kα and Eβ vanishes...

Similarly (R3)
(R4) identifies
    the commutator of Eα and Fβ
    with an element in the subalgebra generated by the K's.

The relations (R5) and (R6) are called quantized Serre relations.