Doi-Hopf module
In quantum group, Hopf algebra and weak Hopf algebra, the Doi-Hopf module is a crucial construction that has many applications. It's named after Japanese mathematician Yukio Doi and German mathematician Heinz Hopf. The concept was introduce by Doi in his 1992 paper "unifying Hopf modules".
Doi-Hopf module
A right Doi-Hopf datum is a triple with a Hopf algebra, a left -comodule algebra, and a right -module coalgebra. A left-right Doi-Hopf -module is a left -module and a right -comodule via such that for all. The subscript is the Sweedler notation.A left Doi-Hopf datum is a triple with a Hopf algebra, a right -comodule algebra, and a left -module coalgebra. A Doi-Hopf module can be defined similarly.