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arXiv · 1504.05057

The dual and the double of a Hopf algebroid are Hopf algebroids

Peter Schauenburg
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Abstract

Let $H$ be a $\times$-bialgebra in the sense of Takeuchi. We show that if $H$ is $\times$-Hopf, and if $H$ fulfills the finiteness condition necessary to define its skew dual $H^\vee$, then the coopposite of the latter is $\times$-Hopf as well. If in addition the coopposite $\times$-bialgebra of $H$ is $\times$-Hopf, then the coopposite of the Drinfeld double of $H$ is $\times$-Hopf, as is the Drinfeld double itself, under an additional finiteness condition.

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Peter Schauenburg. 2015-04-20. The dual and the double of a Hopf algebroid are Hopf algebroids. https://arxiv.org/abs/1504.05057

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