Prime and semiprime quantum linear space smash products

TL;DR

This paper establishes conditions under which smash products involving bosonizations of quantum linear spaces are prime or semiprime, extending previous results on Taft algebras to quantum affine spaces.

Contribution

It provides new criteria for (semi)primeness of smash products with quantum linear spaces, broadening the understanding of their algebraic properties.

Findings

Conditions for (semi)primeness of smash products established

Extended results from Taft algebras to quantum affine spaces

Identified classes of 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.