Superderivation Algebras of Modular Lie Superalgebras of (O)-Type

The authors consider a family of finite-dimensional Lie superalgebras of O-typeover an algebraically closed field of characteristic p > 3. It is proved that the Lie superalgebrasof O-type are simple and the spanning sets are determined. Then the spanningsets are employed to characterize the superderivation algebras of these Lie superalgebras.Finally, the associative forms are discussed and a comparison is made between these Liesuperalgebras and other simple Lie superalgebras of Cartan type.