Braided coproduct, antipode and adjoint action for U_q(sl_2)

Motivated by our attempts to construct an analogue of the Dirac operator in the setting of U_q(𝔰𝔩_n), we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra U_q(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.