Graded automorphisms of quantum affine spaces

TL;DR

This paper determines the structure of the automorphism group of quantum affine spaces, showing it is a semi-direct product of certain matrix and permutation groups, advancing understanding of their symmetries.

Contribution

It explicitly computes the graded automorphism group of quantum affine spaces, revealing its semi-direct product structure, which was previously unknown.

Findings

Automorphism group is isomorphic to a semi-direct product

Identifies the automorphism group as a blocked diagonal matrix group combined with permutations

Provides a complete description of symmetries of quantum affine spaces

Abstract

This paper computes the graded automorphism group of quantum affine spaces. Specifically, we determine that this group is isomorphic to a semi-direct product of a blocked diagonal matrix group and a permutation group.