Abstract
A Lie algebra is said to be perfect when it coincides with its derived subalgebra. The paper is devoted to give a complete structure of covers of perfect Lie algebras. Also, similar to a result of Alperin and Gorenstein (1966) in group theory, it is shown that every automorphism of a finite dimensional perfect Lie algebra may be lifted to an automorphism of its cover. Moreover, we present the concepts of irreducible and primitive extensions of an arbitrary Lie algebra and give some equivalent conditions for a central extension to be irreducible or primitive. Finally, we study the connection between the primitive extensions and the stem covers of finite dimensional perfect Lie algebras.
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