A Class Of Superderivations Subalgebras And Central Factor Superalgebras

Let L=L₁（?）L₀ be a Lie superalgebra over field F.Write ID^*（L）for the Lie superalgebra consisting of superderivations mapping L to L² and central elements to zero.In this article we first give a upper bound for the superdimension of ID^*（L）.Then we characterize the ID^*-superderivation algebras for nilpotent Lie superalge-bras of class 2 and model filiform Lie superalgebras.Finally,We give an upper bound for the superdimension of center factor Lie superalgebra L/Z_n（L）in terms of the superdimension of Ln+i and Z_n（L）,where Z_n（L）and Lⁿ⁺¹ are the n-th and（n+1）-th terms of the upper and lower central series of L,respectively.