Full automorphism groups of the axial algebra for $M_{11}$ and related algebras

TL;DR

This paper determines the full automorphism groups of certain 286-dimensional axial algebras related to the Mathieu group M11 and other algebraic structures, using a hybrid computational and manual approach.

Contribution

It extends previous work by computing automorphism groups of larger, more complex algebras that were not accessible by automatic methods alone.

Findings

Automorphism group of the M11-related algebra computed

Automorphism groups of subalgebras for L_2(11) and A_6 determined

Hybrid computational and manual methods developed for large algebras

Abstract

In this paper, in continuation of arXiv:2311.18538, we compute the full automorphism groups of the 286-dimensional algebra for $M_{11}$, its subalgebras and other related algebras. This includes, in particular, the 101-dimensional algebra for $L_2(11)$ and the 76-dimensional algebra for $A_6$. While smaller algebras can be handled by the fully automatic nuanced method from arXiv:2311.18538, the larger algebras, mentioned above, require a hybrid method combining computation with hand-made proofs.