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We introduce a notion of split extension of (non-associative) bialgebras. We show that this definition is equivalent to the notion of action of (non-associative) bialgebras. We particularize this equivalence to… Click to show full abstract
We introduce a notion of split extension of (non-associative) bialgebras. We show that this definition is equivalent to the notion of action of (non-associative) bialgebras. We particularize this equivalence to (non-associative) Hopf algebras by defining split extensions of (non-associative) Hopf algebras and proving that they are equivalent to actions of (non-associative) Hopf algebras. Moreover, we prove the validity of the Split Short Five Lemma for these kinds of split extensions, and we examine some examples.
Journal Title: Applied Categorical Structures
Year Published: 2021
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