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CitationHalıcı, S., Karataş, A. & Sütlü, S. S. (2020). Hom-lie-hopf algebras. Journal of Algebra, 553, 26-88. doi:10.1016/j.jalgebra.2020.01.022
We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (α,β)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (α,Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras.
SourceJournal of Algebra
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