Abstract: We gave some basic properties of the generalized derivation algebra GDer(L), quasiderivation algebra QDer(L), centroid C(L), quasicentroid QC(L) and central derivation algebra ZDer(L) of a HomLeibniz algebra L. We also proved that QDer(L) could be embedded and become a larger derivation of HomLeibniz algebra.

Key words:  HomLeibniz algebra, generalized derivation, centroid, quasiderivation