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arXiv · 1910.07920

Hom-Lie-Hopf algebras

S. Halici·A. Karataş·S. Sütlü
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Abstract

We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general $(\alpha,\beta)$-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of $(\alpha,{\rm Id})$-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.

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S. Halici, A. Karataş, S. Sütlü. 2019-10-17. Hom-Lie-Hopf algebras. https://arxiv.org/abs/1910.07920

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