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I am study the representation theory of the big quantum group at a root of unity, and I am wonder if it is known a complete classification of the indecomposable modules for it. To be more specific, because the general question is hard to answer, Is it known a complete classification of indecomposable modules for the big quantum group of $\mathfrak{sl}_2$ ? I know there is a classification for the small quantum group of $\mathfrak{sl}_2$, ("Indecomposable restricted representations for quantum $\mathfrak{sl}_2$, Chari & Premet), but for the big, I could't find any answer.

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    $\begingroup$ By biq quantum group you mean Lusztig's version of it? $\endgroup$ – Julian Kuelshammer Aug 3 '18 at 9:25
  • $\begingroup$ Yes @JulianKuelshammer, It is the Lusztig's version of the quantum group. $\endgroup$ – JC Arias Aug 3 '18 at 13:11

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