OPPOSITE SKEW COPAIRED HOPF ALGEBRAS
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Abstract
Let A be a Hopf algebra with a linear form σ : k → A⊗A, which is convolution invertible, such that σ21(∆⊗id)τ (σ(1)) = σ32(id ⊗ ∆)τ (σ(1)). We define Hopf algebras, (Aσ, m, u, ∆σ , ε, Sσ). If B and C are opposite skew copaired Hopf algebras and A = B ⊗k C then we find Hopf algebras, (A[σ], mB ⊗ mC , uB ⊗ uC , ∆[σ], εB ⊗ εC , S[σ]). Let H be a finite dimensional commutative Hopf algebra i }, and let A = H op ⊗ H ∗. We show with dual basis {hi} and {h∗ that if we define σ : k → H op ⊗ H ∗ by σ(1) = P hi ⊗ h∗ i then (A[σ], mA, uA, ∆[σ], εA, S[σ]) is the dual space of Drinfeld double, D(H)∗, as Hopf algebra.
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