Applied Categorical Structures

, Volume 25, Issue 1, pp 147–154 | Cite as

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

  • Peter SchauenburgEmail author


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.


Bialgebroid Hopf algebroid Duality 

Mathematics Subject Classifications (2010)

16T99 18D10 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bourgogne, UMR5584 CNRSUniversité Bourgogne Franche-ComtéDijonFrance

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