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Journal Article

Bicrossed products with the Taft algebra

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Agore,  A. L.
Max Planck Institute for Mathematics, Max Planck Society;

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Năstăsescu,  L.
Max Planck Institute for Mathematics, Max Planck Society;

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arXiv:1712.06095.pdf
(Preprint), 159KB

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Citation

Agore, A. L., & Năstăsescu, L. (2019). Bicrossed products with the Taft algebra. Archiv der Mathematik, 113(1), 21-36. doi:10.1007/s00013-019-01328-3.


Cite as: http://hdl.handle.net/21.11116/0000-0004-6829-A
Abstract
Let $G$ be a group which admits a generating set consisting of finite order elements. We prove that any Hopf algebra which factorizes through the Taft algebra and the group Hopf algebra $K[G]$ (equivalently, any bicrossed product between the aforementioned Hopf algebras) is isomorphic to a smash product between the same two Hopf algebras. The classification of these smash products is shown to be strongly linked to the problem of describing the group automorphisms of $G$. As an application, we completely describe by generators and relations and classify all bicrossed products between the Taft algebra and the group Hopf algebra $K[D_{2n}]$, where $D_{2n}$ denotes the dihedral group.