Braided coproduct, antipode and adjoint action for Uq (sl₂)

Motivated by our attempts to construct an analogue of the Dirac operator in the setting of Uq (slₙ), we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra Uq (sl₂). The braided adjoint action is seen to coincide with the ordinary quantum adjoint action, which also follows from the general results of S. Majid.