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On \(\pi\)-twisted smash coproducts and \(\pi\)-\(L\)-\(R\) smash coproducts. (Chinese. English summary) Zbl 1212.16068

Summary: The notions of \(\pi\)-smash coproducts, \(\pi\)-twisted smash coproducts and \(\pi\)-\(L\)-\(R\) smash coproducts are introduced. It is proved that they are all \(\pi\)-coalgebras, and a necessary condition for \(\pi\)-smash coproducts to be Hopf \(\pi\)-coalgebras is given. For any finite type Hopf \(\pi\)-coalgebras, it is proved that there exists a \(\pi\)-coalgebra isomorphism between \(\pi\)-twisted smash coproducts and \(\pi\)-\(L\)-\(R\) smash coproducts if each \(H_\alpha\) is commutative.

MSC:

16T15 Coalgebras and comodules; corings
16S40 Smash products of general Hopf actions
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