# Actions of quantum linear spaces on quantum algebras

## TL;DR

This paper classifies how quantum linear spaces act on quantum algebras, providing bounds and showing triviality of certain actions, advancing understanding of quantum symmetries.

## Contribution

It offers a classification of actions of bosonizations of quantum linear spaces on quantum algebras, including bounds on their rank and triviality results.

## Key findings

- All actions of generalized Taft algebras on quantum affine spaces are trivial extensions.
- Bounds are established on the rank of bosonizations acting on quantum algebras.
- Classification results for actions on quantum affine spaces and quantum matrix algebras.

## Abstract

We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras are trivial extensions of actions on quantum planes. In both cases we achieve bounds on the rank of the bosonization acting on the algebra.