The Launois-Lenagan conjecture

TL;DR

This paper proves the Launois-Lenagan conjecture, classifying automorphism groups of quantum matrix algebras for all sizes, base fields, and generic deformation parameters.

Contribution

It provides a complete proof of the conjecture, extending the classification to all positive integers n and non-root of unity q.

Findings

Automorphism groups of quantum matrix algebras are fully classified.

The classification holds for all positive integers n and base fields K.

The result applies to all deformation parameters q not roots of unity.

Abstract

In this note we prove the Launois-Lenagan conjecture on the classification of the automorphism groups of the algebras of quantum matrices R_q[M_n] of square shape for all positive integers n, base fields K, and deformation parameters q \in K^* which are not roots of unity.