Stabilizing Automorphisms of Quantum Affine Space

TL;DR

This paper classifies the automorphism groups of quantum affine spaces up to dimension 7, exploring their structure via permutation actions, decompositions, and tensor products, advancing understanding of their symmetries.

Contribution

It provides a comprehensive classification of graded automorphism groups for quantum affine spaces of dimension 7 or less, including their decompositions and tensor product structures.

Findings

Classified automorphism groups for spaces up to dimension 7

Identified conditions for group decompositions via permutation actions

Described automorphism groups arising from tensor products of quantum parameters

Abstract

We examine the graded automorphism groups of quantum affine spaces and classify these groups for spaces of dimension 7 or less. Using permutation actions on partitions, we investigate cases when the group decomposes as a product of graded automorphism groups of smaller dimensional spaces, and we describe the groups arising from the Kronecker tensor product of independent quantum parameter matrices.