On Perfect Lie Superalgebras And Low Dimensional Lie Superalgebras

The purposes of this paper are to discuss some properties of perfect Lie superalgebras and to determine the types of low dimensional Lie superalgebras over any field of characteristic≠2.In Section 2,it is proved that the derivation superalgebra of a centerless perfect Lie superalgebra of finite dimension over any field is complete.Then we give a necessary and sufficient condition of the holomorph of a centerless perfect Lie superalgebra to be complete.In particular,we find some relations between complete Lie superalgebras and perfect Lie superalgebras.In Section 3,some interesting properties of perfect restricted Lie superalgebras are investigated.The last section is devoted to the determination of Lie superalgebras of dimension two and three by the method of undetermined coefficient.