Of Cartan Mold Of Lie Superalgebra W (m; N; (?)) Of The Second Order Cohomology Group

Let F be a algebracially closed field and charF = p > 2.In this paper, the cohomology group H2(W(m; n; i), F) of finite dimensional modular simple Lie superalgebra W(m;n;t) over F is determined. The main results are following:L - 0 Ll is assumed to be a finite dimensional graded Lie su-i=-rperalgebra over FLemma 3.4 Suppose thata)L = U(L-)-Lqb)Lg is an irreducible L0-moduleLet ~f : L L' be a homogeneous skew ,where - 2q r - q, (f defines an element of ker , then is inner.2) If / = r - q. (p is skew and defines an element of ker i, then is inner.Lemma 4.5 Suppose that H C LQ is a nilpotent subalgebra and assume that L - U(L~) ?Lq. Let be skew derivation of degree (/.0).which defines an element of ker. Then the following statements hold:1) If - q < I < r - q- 1, then is inner.2) If / = -q and A9 f o = 0, then is inner.Theory 5.2 The second cohomology group H2(W(m.; n;t), F) is trivial, where m, n > 2.