An algebraic framework for the Drinfeld double based on infinite groupoids

In this paper we mainly consider the notion of Drinfeld double for two weak multiplier Hopf (⁎-)algebras which are paired with each other. Then we show that the Drinfeld double is again a weak multiplier Hopf (⁎-)algebra. Furthermore, we study integrals on the Drinfeld double. Finally, we establish...

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Bibliographic Details
Published in:Journal of algebra 2024-06, Vol.647, p.633-683
Main Authors: Zhou, Nan, Wang, Shuanhong
Format: Article
Language:English
Subjects:
Drinfeld double
Infinite groupoid
Weak multiplier Hopf algebra
Yetter-Drinfeld module
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Summary:In this paper we mainly consider the notion of Drinfeld double for two weak multiplier Hopf (⁎-)algebras which are paired with each other. Then we show that the Drinfeld double is again a weak multiplier Hopf (⁎-)algebra. Furthermore, we study integrals on the Drinfeld double. Finally, we establish the correspondence between modules over a Drinfeld double D(A) and Yetter-Drinfeld modules over a weak algebraic quantum group A.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2024.02.017