New examples of Green functors arising from representation theory of semisimple Hopf algebras

TL;DR

This paper explores a Mackey type decomposition for representations of semisimple Hopf algebras, introducing new Green functors derived from gradings on corepresentation categories, expanding the theoretical framework in representation theory.

Contribution

It demonstrates a general Mackey type decomposition for semisimple Hopf algebra representations and constructs new Green functors from category gradings.

Findings

Decomposition occurs when modules are induced from Hopf subalgebras and restricted to group subalgebras.

New examples of Green functors are constructed from gradings on corepresentation categories.

The results extend the understanding of representation theory for semisimple Hopf algebras.

Abstract

A general Mackey type decomposition for representations of semisimple Hopf algebras is investigated. We show that such a decomposition occurs in the case that the module is induced from an arbitrary Hopf subalgebra and it is restricted back to a group subalgebra. Some other examples when such a decomposition occurs are also constructed. They arise from gradings on the category of corepresentations of a semisimple Hopf algebra and provide new examples of Green functors in the literature.