We show that the braided tensor category of finitely-generated weight modules for the simple affine vertex operator algebra \(L_k(\mathfrak {sl}_2)\) of \(\mathfrak {sl}_2\) at any admissible level k is rigid and hence a braided ribbon category. The proof uses a recent result of the first two authors with Shimizu and Yadav on embedding a braided Grothendieck-Verdier category \(\mathcal {C}\) into the Drinfeld center of the category of modules for a suitable commutative algebra A in \(\mathcal {C}\) , in situations where the braided tensor category of local A-modules is rigid. Here, the commutative algebra A is Adamović’s inverse quantum Hamiltonian reduction of \(L_k(\mathfrak {sl}_2)\) , which is the simple rational Virasoro vertex operator algebra at central charge \(1-\frac{6(k+1)^2}{k+2}\) tensored with a half-lattice conformal vertex algebra. As a corollary, we also show that the category of finitely-generated weight modules for the \(N = 2\) super Virasoro vertex operator superalgebra at central charge \(-6\ell -3\) is rigid for \(\ell \) such that \((\ell +1)(k+2) = 1\) .
