Locally Finite Representations Over Noetherian Hopf algebras

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.

revised version after acceptance in PAMS; Theorem 4.5 removed and Theorem 2.9 improved

References in corpus (2)

• Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two
• Simple modules and their essential extensions for skew polynomial rings

Cited by in corpus (1)

• The finite dual coalgebra as a quantization of the maximal spectrum