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The generalized Lie algebras, which have recently been introduced under the name of color (super) algebras, are investigated. The generalized Poincaré–Birkhoff–Witt and Ado theorems hold true. We discuss the so-called commutation factors which enter into the defining identities of these algebras. Moreover, we establish a close relationship between the generalized Lie algebras and ordinary Lie (super) algebras.
M. Scheunert (Sun,) studied this question.