Partial Hopf actions, partial invariants and a Morita context

2009/01/08 by Alves, Marcelo Muniz S., Eliezer Batista, Batista, Eliezer · 2 citations
Mathematics · #16S35 (Secondary) #16S40 #16W30 (Primary) #57T05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0901.0959

openalex publication_date 2009/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to assure the existence of enveloping actions. This allows to extend several results from the theory of partial group actions to the Hopf algebraic setting. In this article, we explore some properties of the fixed point subalgebra with relations to a partial action of a Hopf algebra. We also construct, for partial actions of finite dimensional Hopf algebras a Morita context relating the fixed point subalgebra and the partial smash product. This is a generalization of a well known result in the theory of Hopf algebras for the case of partial actions. Finally, we study Hopf-Galois extensions and reobtain some classical results in the partial case.

Cited by

• A class of twisted partial Hopf actions
• Partial Representations of Hopf Algebras

Related

• Enveloping Actions for Partial Hopf Actions
• Morita equivalence and globalization for partial Hopf actions on nonunital algebras
• Globalization theorems for partial Hopf (co)actions, and some of their applications
• Partial (Co)Actions of Multiplier Hopf Algebras: Morita and Galois Theories
• Partial Actions of a Hopf algebra on its base field and the corresponding partial smash product algebra