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Pré-Publication, Document De Travail Année : 2015

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

Résumé

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, 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.

Dates et versions

hal-01144711 , version 1 (22-04-2015)

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Peter Schauenburg. The dual and the double of a Hopf algebroid are Hopf algebroids. 2015. ⟨hal-01144711⟩
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