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

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, 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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https://hal.archives-ouvertes.fr/hal-01144711
Contributor : Peter Schauenburg <>
Submitted on : Wednesday, April 22, 2015 - 3:16:53 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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  • HAL Id : hal-01144711, version 1
  • ARXIV : 1504.05057

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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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