  The quantized enveloping algebra $U_q$ is constructed as a quotient of the
generalized 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 $\cmdcalD = (\cmdfrakB (V) \cmddotrtimes
F) \cmdbicross_{\tau} (\cmdfrakB (W) \cmddotrtimes G)$, where $F$, $G$ are
abelian groups, $ V \in {}^F_F \cmdcalYD $, $ W \in {}^G_G \cmdcalYD $ are
Yetter-Drinfeld modules and $ \cmdfrakB (V) $, $ \cmdfrakB (W) $ are their
Nichols algebras. We prove some results on Hopf ideals of $ \cmdcalD $,
including a characterization of what we call thin Hopf ideals. As an
application we give an explicit description of those minimal quasitriangular
pointed Hopf algebras in characteristic zero which are generated by skew
primitives.
