Abstract
Let H be a ×-bialgebra in the sense of Takeuchi. We show that if H is ×-Hopf, and if H fulfills the finiteness condition necessary to define its skew dual H ∨, then the coopposite of the latter is ×-Hopf as well. If in addition the coopposite ×-bialgebra of H is ×-Hopf, then the coopposite of the Drinfeld double of H is ×-Hopf, as is the Drinfeld double itself, under an additional finiteness condition.
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Schauenburg, P. The Dual and the Double of a Hopf Algebroid are Hopf Algebroids. Appl Categor Struct 25, 147–154 (2017). https://doi.org/10.1007/s10485-015-9418-7
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DOI: https://doi.org/10.1007/s10485-015-9418-7