论文标题
Bialgebras和Hopf代数的分裂扩展和动作
Split extensions and actions of bialgebras and Hopf algebras
论文作者
论文摘要
我们介绍了（非缔合性）双重骨的分裂延伸概念，该概述概括了M. Gran，G。Janelidze和M. Sobral引入的岩浆的分裂延伸概念。我们表明，该定义等同于（非缔合性）双gebras的作用概念。我们通过定义（非缔合性）Hopf代数的分裂扩展，并证明它们等于（非缔合性）Hopf代数的行为，从而将这种等价与（非缔合性的）Hopf代数相等。此外，我们证明了这些类型的分裂扩展的分裂短五引理的有效性，并研究了一些示例。
We introduce a notion of split extension of (non-associative) bialgebras which generalizes the notion of split extension of magmas introduced by M. Gran, G. Janelidze and M. Sobral. 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.
