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

By Stefaan Caenepeel, K. Janssen. 2006

108 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/87a263ff163f99f15fef5142de112c403f7dcf3a

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In Algebra and Number Theory

1. Marcelo Muniz Silva Alves
2. Eliezer Batista
3. Mikhailo Dokuchaev

In Geometry and Topology

1. Marcelo Muniz Silva Alves
2. Eliezer Batista
3. Mikhailo Dokuchaev

In Mathematical Physics

1. Marcelo Muniz Silva Alves
2. Eliezer Batista
3. Mikhailo Dokuchaev

Citations in the corpus

• Globalization theorems for partial Hopf (co)actions, and some of their applications (2010, methodology): “This example of partial coaction comes from [4].”
• Enveloping Actions for Partial Hopf Actions (2008, methodology): “Afterwards, Caenepeel and Janssen defined partial actions and partial coactions of a Hopf algebra H on a unital algebra A using the notions of partial entwining structures [ 4 ]; in particular, partial actions of G determine partial actions of the group algebra kG in a natural way.”