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Braided coproduct, antipode and adjoint action for $U_q(sl_2)$
Archivum mathematicum, Tome 60 (2024) no. 5, pp. 365-376 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2024-5-365
Classification : 16T20, 20G42
Keywords: quantum group; quantum $\mathfrak{sl}_2$; quantum adjoint action; tensor categories; braided tensor product; braided adjoint action 
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Pandžić, Pavle; Somberg, Petr. Braided coproduct, antipode and adjoint action for $U_q(sl_2)$. Archivum mathematicum, Tome 60 (2024) no. 5, pp. 365-376. doi: 10.5817/AM2024-5-365

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