quasicentroid

The main results are: for all 3-Lie algebra A, 1) the generalized derivation algebra GDer(A) is the sum of quasiderivation algebra QDer(A) and quasicentroid Q𝛤(A); 2) quasiderivations of A can be embedded as derivations in a larger algebra; 3) quasiderivation algebra QDer(A) normalizer quasicentroid, that is, [QDer(A),Q𝛤(A)]⊆Q𝛤(A); 4) if A contains a maximal diagonalized tours T, then QDer(A) and Q𝛤(A) are diagonalized T-modules, that is, as T-modules, (T,T) semi-simplely acts on QDer(A) and Q𝛤(A), respectively..