Derivations for the even part of the Hamiltonian superalgebra in positive characteristic

In this paper we consider the derivations for even part of the finitedimensional Hamiltonian superalgebra H over a field of prime characteristic. We first introduce an ideal N of H 0 and show that the derivation space from H 0 into W 0 can be obtained by the derivation space from N into W 0 , the even part of the generalized Witt superalgebra W . For further application we also give the generating set of the ideal N. Then we describe three series of exceptional derivations from H 0 intoW 0 . Finally, we determine all the derivations vanishing on the non-positive Z-graded part of H 0 , the odd Z-homogeneous derivations, and negative Z-homogeneous derivations from H 0 into W 0 . Mathematics Subject Classification 2000: 17B50, 17B40