Twisting products of Hopf algebras and quantum double

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Let σ be a skew pairing on the pair (B, H) of Hopf algebras, and A a left(B, H) bicomodule algebra. A new algebra A_σ, called the twisting product of A, is obtained by alternating the multiplication of A using σ and the coactions on A by B and H. σ induce
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