Simple algebras and the analogue of classical invariant theory for nonclassical groups

Two topics will be discussed:

• (1) If a $G$-module $V$ admits a structure of a simple algebra $A$ such that $G={\rm Aut}\,A$, then there is a close approximation to the analogue of classical invariant theory for $V$.
• (2) What are the groups $G$ that appear in this way?