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

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• 作者：Peter Schauenburg
• 关键词：Bialgebroid ; Hopf algebroid ; Duality
• 刊名：Applied Categorical Structures
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：25
• 期：1
• 页码：147-154
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematical Logic and Foundations; Theory of Computation; Convex and Discrete Geometry; Geometry;
• 出版者：Springer Netherlands
• ISSN：1572-9095
• 卷排序：25

文摘

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.