Every 2-dimensional braided Hopf algebra over a quasi-Hopf algebra H is either the trivial k[C2] or a member of the explicitly parametrized family B_{σ,v}.
Abe, ”Hopf algebras”, Cambridge: Cambridge University Press 1977
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Biproduct Quasi-Hopf Algebras of Rank 2
Every 2-dimensional braided Hopf algebra over a quasi-Hopf algebra H is either the trivial k[C2] or a member of the explicitly parametrized family B_{σ,v}.