Braided coproduct, antipode and adjoint action for $U_q(s{l}_2)$

Abstract

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.

Accepted to Archivum Mathematicum