A duality theorem for weak multiplier Hopf algebra actions

作者：Zhou, Nan; Wang, Shuanhong^*

来源：International Journal of Mathematics, 2017, 28(5): 1750032.

DOI：10.1142/S0129167X1750032X

• Duality theorem
• weak multiplier Hopf algebras
• actions
• groupoids

The main purpose of this paper is to unify the theory of actions of Hopf algebras, weak Hopf algebras and multiplier Hopf algebras to one of actions of weak multiplier Hopf algebras introduced by Van Daele and Wang. Using such developed actions, we will define the notion of a module algebra over weak multiplier Hopf algebras and construct their smash products. The main result is the duality theorem for actions and their dual actions on the smash product of weak multiplier Hopf algebras. As an application, we recover the main results found in the literature for weak Hopf algebras, multiplier Hopf algebras and groupoids.

• 出版日期2017-5
• 单位东南大学