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The quantized enveloping algebra $U_q$ is constructed as a quotient of thegeneralized quantum double $ U^{\leq 0}_q \cmdbicross_{\tau} U^{\geq 0}_q $associated to a natural skew pairing $ \tau : U^{\leq 0}_q \otimes U^{\geq 0}_q\to k $. This double is generalized by $\cmdcalD = (\cmdfrakB (V) \cmddotrtimesF) \cmdbicross_{\tau} (\cmdfrakB (W) \cmddotrtimes G)$, where $F$, $G$ areabelian groups, $ V \in {}^F_F \cmdcalYD $, $ W \in {}^G_G \cmdcalYD $ areYetter-Drinfeld modules and $ \cmdfrakB (V) $, $ \cmdfrakB (W) $ are theirNichols algebras. We prove some results on Hopf ideals of $ \cmdcalD $,including a characterization of what we call thin Hopf ideals. As anapplication we give an explicit description of those minimal quasitriangularpointed Hopf algebras in characteristic zero which are generated by skewprimitives.

Hopf ideals of the generalized quantum double associated to skew-paired Nichols algebras