Levi decomposition of a quiver automorphism group

Fixing a Krull-Schmidt decomposition embeds $L={\prod }_a{\mathrm{GL}}_{m_a}(k)$ by its actions on multiplicity spaces. This splits reduction modulo the Jacobson radical. Hence ${\mathrm{Aut}}_Q(X)=(1+J({\mathrm{End}}_Q(X)))⋊L$, with a closed normal unipotent first factor. The explicit section works in every characteristic.