Is it possible to classify Hopf algebras $H$, over a field $k$, which admit a unique (up to isomorphism) irreducible comodule, namely the trivial $1$-dim comodule $$ k \to k \otimes H, ~~ v \mapsto v \otimes 1_H. $$
Classifying Hopf algebras that admit a single irreducible comodule
Spyros Olympopolous
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