Isoclinism in Lie superalgebras

In this paper using the concept of isoclinism, we give the structure of all covers of Lie superalgebras when their Schur multipliers are finite dimensional. Further it has been shown that, each stem extension of a finite dimensional Lie superalgebra is a homomorphic image of a stem cover for it and as a corollary it is concluded that maximal stem extensions of Lie superalgebras are precisely same as the stem covers. Moreover, we have defined stem Lie superalgebra and show that a Lie superalgebra with finite dimensional derived subalgebra and finitely generated central factor is isoclinic to a finite dimensional Lie superalgebra