Quantized enveloping algebras
(from Jantzen:
Quantum Groups
)
(R2) means:
the q
(α,β)
-commutator
of K
α
and E
β
vanishes...
Similarly (R3)
(R4) identifies
the commutator of E
α
and F
β
with an element in the subalgebra generated by the K's.
The relations (R5) and (R6) are called quantized Serre relations.