Locally Finite Representations Over Noetherian Hopf algebras

TL;DR

This paper investigates the structure of locally finite representations over Noetherian Hopf algebras, providing criteria for their closure properties and extending known results to broader classes of algebras.

Contribution

It establishes necessary and sufficient conditions for the closure of locally finite representations under injective hulls in Noetherian Hopf algebras, extending prior results to Ore extensions and affine Hopf algebras.

Findings

Criteria for closure under injective hulls in Noetherian Hopf algebras

Extension of known results to Ore extensions and Hopf crossed products

Characterization of locally finite representations in low Gelfand-Kirillov dimension

Abstract

We study finite dimensional representations over some Noetherian algebras over a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category of locally finite dimensional representations to be closed under taking injective hulls and extend results known for group rings and enveloping algebras to Ore extensions, Hopf crossed products and affine Hopf algebras of low Gelfand-Kirillov dimension.