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We classify exact indecomposable module categories over the representation category of all non-trivial Hopf algebras with coradi- cal S3 and S4. As a byproduct, we compute all its Hopf-Galois extensions and we show that these Hopf algebras are cocycle deformations of their graded versions.

Representations of the category of modules over pointed Hopf algebras over 𝕊3and 𝕊4

Representations of the category of modules over pointed Hopf algebras over 𝕊₃and 𝕊₄