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arXiv · 1701.00665

A note on split extensions of bialgebras

Xabier García-Martínez·Tim Van der Linden
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Abstract

We prove a universal characterization of Hopf algebras among cocommutative bialgebras over a field: a cocommutative bialgebra is a Hopf algebra precisely when every split extension over it admits a join decomposition. We also explain why this result cannot be extended to a non-cocommutative setting.

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Xabier García-Martínez, Tim Van der Linden. 2017-03-13. A note on split extensions of bialgebras. https://doi.org/10.1515/forum-2017-0016

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