Partial corepresentations of Hopf Algebras

2019/11/20 by Alves, Marcelo Muniz S ., Batista, Eliezer, Castro, Felipe +2 · 1 citation
#16S40 #16T05 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1911.09141

Abstract

We introduce the notion of a partial corepresentation of a given Hopf algebra H over a coalgebra C and the closely related concept of a partial H-comodule. We prove that there exists a universal coalgebra H^par, associated to the original Hopf algebra H, such that the category of regular partial H-comodules is isomorphic to the category of H^par-comodules. We introduce the notion of a Hopf coalgebroid and show that the universal coalgebra H^par has the structure of a Hopf coalgebroid over a suitable coalgebra.

Cited by

• Globalization and the biactegory of partial modules

Related

• Partial Representations of Hopf Algebras
• Partial Coactions of Weak Hopf Algebras on Coalgebras
• Dual Constructions for Partial Actions of Hopf Algebras
• Towards a classification of simple partial comodules of Hopf algebras
• A comonadicity theorem for partial comodules