Partial Representations of Hopf Algebras

2013/09/06 by Alves, Marcelo Muniz S., Batista, Eliezer, Vercruysse, Joost
#16S35 #16S40 #16T05 #16W50 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1309.1659

Abstract

In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra H, one can associate it to a Hopf algebroid H_par which has the universal property that each partial representation of H can be factorized by an algebra morphism from H_par. We define also the category of partial modules over a Hopf algebra H, which is the category of modules over its associated Hopf algebroid H_par. The Hopf algebroid structure of H_par enables us to enhance the category of partial H modules with a monoidal structure and such that the algebra objects in this category are the usual partial actions. Some examples of categories of partial H modules are explored. In particular we can describe fully the category of partially ℤ₂-graded modules.

Related

• Weak Partial Representations
• Partial Hopf module categories
• On partial representations of pointed Hopf algebras
• Partial Hopf-Galois theory
• Dual Constructions for Partial Actions of Hopf Algebras