This question asks for the term 'special' automorphism' used in Encyclopedia of Mathematics' entry describing a quaternionic structure. As I have posted in other questions, a quaternionic structure on a $4n$-dimensional real vector space $V$ is a vector subspace (subalgebra) $Q\subset End(V)$ spanned by the identity and two anticommuting complex structures $J_1$ and $J_2$:
$$ Q=span_\mathbb R\{id_V,J_1,J_2,J_1J_2\} $$
(I usually ignore the identity and regard $Q$ as a 3-dimensional algebra, but since it is globally defined on any tangent bundle I think that does not matter actually).
Now, the Encyclopedia says:
An automorphism $A$ of the vector space $V$ is called an automorphism of the quaternionic structure if the transformation $Ad A$ of the space of automorphisms induced by it preserves $Q$, that is, if $Ad A(Q)=AQA^{-1}=Q$. If, moreover, the identity automorphism is induced on $Q$, then $A$ is called a special automorphism of the quaternionic structure.
As a result, it says that the gruop of all special automorphisms of the quaternionic structure $Q$ is isomorphic to the general linear group $GL(n,\mathbb H)$ over the skew-field $\mathbb H$. In differential geometry, I know this means that your two almost complex structures $J_1$ and $J_2$ are globally defined, something that may not happen in quaternionic manifolds (in the sense that the structure group reduces to $GL(n,\mathbb H)GL(1,\mathbb H)$). But it seems that in the linear case you can also have two different groups depending on if the identity automorphism is induced on $Q$ or not. And that is what I do not understand.
Question. What does ''the identity automorphism is induced on $Q$'' mean?