The Dual and the Double of a Hopf Algebroid are Hopf Algebroids

Abstract : Let $H$ be a x-bialgebra in the sense of Takeuchi. We show that if $H$ is x-Hopf, and if $H$ fulfills the finiteness condition necessary to define its skew dual $H^\vee$, then the coopposite of the latter is x-Hopf as well. If in addition the coopposite x-bialgebra of $H$ is x-Hopf, then the coopposite of the Drinfeld double of $H$ is x-Hopf, as is the Drinfeld double itself, under an additional finiteness condition.
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Submitted on : Monday, March 27, 2017 - 7:11:20 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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Peter Schauenburg. The Dual and the Double of a Hopf Algebroid are Hopf Algebroids. Applied Categorical Structures, Springer Verlag (Germany), 2017, 25 (1), pp.147 - 154. ⟨10.1007/s10485-015-9418-7⟩. ⟨hal-01496801⟩

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