Partial (Co)Actions of Hopf Algebras and Partial Hopf-Galois Theory

Abstract

We introduce partial (co)actions of a Hopf algebra H on an algebra. To this end, we introduce first the notion of lax coring, generalizing Wisbauer's notion of weak coring. We also have the dual notion of lax ring. Several duality results are given, and we develop Galois theory for partial H-comodule algebras.

Key Words:

• Coring
• Entwining structure
• Galois extension
• Smash product

2000 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENT

This research was supported by the research project G.0622.06 “Deformation quantization methods for algebras and categories with applications to quantum mechanics” from FWO-Vlaanderen.

Notes

Communicated by R. Wisbauer.