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Keywords:
quantum group; quantum $\mathfrak{sl}_2$; quantum adjoint action; tensor categories; braided tensor product; braided adjoint action
quantum group; quantum $\mathfrak{sl}_2$; quantum adjoint action; tensor categories; braided tensor product; braided adjoint action
Summary:
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.
References:
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