Hopf Modules in the Category of Yetter-Drinfeld Modules

Yanmin Yin

doi:10.4236/am.2016.77058

Abstract

We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf module structure in the Yetter-Drinfeld category. As an application we deduce the existence and uniqueness of right integral from it.

Highlights

Weak Hopf algebras were introduced by G
The main difference between ordinary and weak Hopf algebras comes from the fact that the comultiplication of the latter is no longer required to preserve the unit and results in the existence of two canonical subalgebras playing the role of “noncommutative bases”
In [7] we prove a Fundamental Theorem of Hopf modules for the categorical weak Hopf algebra motivation to study quasitriangular weak Hopf algebras is the so-called biproduct construction and interpreted in the terms of braided categories

Summary

Introduction

Weak Hopf algebras were introduced by G. In [7] we prove a Fundamental Theorem of Hopf modules for the categorical weak Hopf algebra motivation to study quasitriangular weak Hopf algebras is the so-called biproduct construction and interpreted in the terms of braided categories. We prove the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules according to the fact that the matrix R gives rise to a natural braiding for L M and LLYD. H * is a right H-Hopf module in the category Yetter-Drinfeld modules. Using this result we obtain the existence and. (2016) Hopf Modules in the Category of Yetter-Drinfeld Modules. Yin uniqueness of integrals for a finite dimensional weak Hopf algebra in LLYD

Preliminaries

Weak Hopf Algebras in the Yetter-Drinfeld Module Category

Applications