Assuming that H is a Hopf algebra o ver a f ield k ,A a right H comodale algebra, σ ∈Hom k ( H ? 獺 , k )is an invertible right 2 cocycle of H ,we define a new multiplication in A and get a twisted alge bra A σ .

If H is a bialgebra over a field k,and σ∈(H×H) * is a strong cocycle,then we can prove the existence of a sub monoidal category μ (H,σ) in μ H ,and several equivalent conditions of μ (H,σ) =μ H .

Based on the different classification of 1-cocycle of the group algebra over dihedral group,the algebra relationship and the Hopf algebra structure of the Hopf Ore extension are provided under the condition of odd and even numbers.