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arXiv · 1407.3835

Wreath products of cocommutative Hopf algebras

Laurent Bartholdi·Olivier Siegenthaler·Todd Trimble
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Abstract

We define wreath products of cocommutative Hopf algebras, and show that they enjoy a universal property of classifying cleft extensions, analogous to the Kaloujnine-Krasner theorem for groups. We show that the group ring of a wreath product of groups is the wreath product of their group rings, and that (with a natural definition of wreath products of Lie algebras) the universal enveloping algebra of a wreath product of Lie algebras is the wreath product of their enveloping algebras. We recover the aforementioned result that group extensions may be classified as certain subgroups of a wreath product, and that Lie algebra extensions may also be classified as certain subalgebras of a wreath product.

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Laurent Bartholdi, Olivier Siegenthaler, Todd Trimble. 2014-07-14. Wreath products of cocommutative Hopf algebras. https://arxiv.org/abs/1407.3835

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