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This work presents a classification of $U_q(\mathfrak{sl}_2)$-symmetries onthe quantum disc. The principal invariant of such classification, the gradingjump, is introduced. It turns out that, under the present subjects, the gradingjump can take only 3 values: $0$, $1$, $-1$. The subcollection of the completecollection of symmetries is extracted in such a way that the selectedsymmetries satisfy certain compatibility condition for involutions.

$U_q\left(\mathfrak{sl}_2\right)$-symmetries of the quantum disc: a complete list