Geodesic
Semisimple Hopf algebras
Čebyševskij sbornik, Tome 15 (2014) no. 1, pp. 19-31

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There is given a survey of results on a structure of semisimple finite dimensional Hopf algebras with isomorphic irreducible non-one-dimensional representations. There is found an explicit form of group-like elements in these Hopf algebras and a structure of the dual a Hopf algebra. 
@article{CHEB_2014_15_1_a2,
     author = {V. A. Artamonov},
     title = {Semisimple {Hopf} algebras},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2014_15_1_a2/}
}
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V. A. Artamonov. Semisimple Hopf algebras. Čebyševskij sbornik, Tome 15 (2014) no. 1, pp. 19-31. http://geodesic.mathdoc.fr/item/CHEB_2014_15_1_a2/