On linearity of automorphism groups of algebras and groups

TL;DR

This paper reviews existing results and approaches to determine whether automorphism groups of algebras and groups are linear or non-linear, providing insights into their structural properties.

Contribution

It synthesizes published findings and outlines methods for analyzing the linearity of automorphism groups of algebras and groups.

Findings

Automorphism groups of certain algebras are linear.

Some automorphism groups are proven to be non-linear.

The paper highlights key approaches for establishing linearity or non-linearity.

Abstract

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.