Categories of modules over semisimple finite-dimensional Hopf algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 5-18.

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There is given a construction of a series of semisimple finite-dimensional Hopf algebras having a single irreducible representation of a dimension greater than $1$. This dimension is equal to the number of one-dimensional representations.
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V. A. Artamonov. Categories of modules over semisimple finite-dimensional Hopf algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 5-18. http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a0/

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