  Motivated by our attempts to construct an analogue of the Dirac operator in
the setting of $U_q(\mathfrak{sl}_n)$, we write down explicitly the braided
coproduct, antipode, and adjoint action for quantum algebra
$U_q(\mathfrak{sl}_2)$. The braided adjoint action is seen to coincide with the
ordinary quantum adjoint action, which also follows from the general results of
S. Majid.
