Almost Inner Derivations of Affinizations of Minimal Q-graded Subalgebras

Minimal Q-graded subalgebras of semisimple Lie algebras are introduced, and it is proved that their derived algebras are abelian. Almost inner derivations of minimal Q-graded subalgebras are investigated, they are all inner derivations. Based on these Lie algebras, a decomposition formula is obtained for derivations of loop algebras, and almost inner derivations of affinizations are determined.