The Even Parts Of The Finite-dimensional Modular Lie Superalgebras Γ

This paper studies the problem of the derivations of the even parts of the finite-dimensional modular Lie superalgebras of Γ-type. Let F be the underlying field of charac-teristic p>3. We know that the even parts of Lie superalgebras can be seen as Lie algebras and they play an important role in the research of the constructions of Lie superalgebras. This paper discusses the generators of the even parts Γ*of modular Lie superalgebras of Γ-type.By giving the generators, and using certain properties of the torus, we describe explicitly the derivation algebra of the even part of Γ*of modular Lie superalgebras Γ.