Prime and semiprime quantum linear space smash products

Abstract

Bosonizations of quantum linear spaces are a large class of pointed Hopf algebras that include the Taft algebras and their generalizations. We give conditions for the smash product of an associative algebra with a bosonization of a quantum linear space to be (semi)prime. These are then used to determine (semi)primeness of certain smash products with quantum affine spaces. This extends Bergen's work on Taft algebras.

Added exposition in introduction. Small changes throughout

References in corpus (3)

• Discriminants of Taft algebra smash products and applications
• When is a smash product semiprime?
• Actions of quantum linear spaces on quantum algebras