Semisimplicity of the Categories of Yetter–Drinfeld Modules and Long Dimodules

Abstract

Let k be a field, and H a Hopf algebra with bijective antipode. If H is commutative, noetherian, semisimple and cosemisimple, then the category _H 𝒴𝒟 ^H of Yetter–Drinfeld modules is semisimple. We also prove a similar statement for the category of Long dimodules, without the assumption that H is commutative.

Key Words:

• Semisimple
• Yetter–Drinfeld module
• Long dimodule

2000 Mathematics Subject Classification:

• 16W30

Acknowledgments

The authors thank the referee for his or her useful comments. Research supported by the project G.0278.01 “Construction and applications of non-commutative geometry: from algebra to physics” from FWO Vlaanderen.

Notes

^#Communicated by M. Cohen.