Derivations of the even part of the odd hamiltonian superalgebra in modular case

In this paper we mainly study the derivations for even part of the finite-dimensional odd Hamiltonian superalgebra HO over a field of prime characteristic. We first give the generating set of the even part g of HO. Then we compute the derivations from g into the even part M of the generalized Witt superalgebra. Finally, we determine the derivation algebra and outer derivation algebra of g and the dimension formulas. In particular, the first cohomology groups H 1(g ; M) and H 1(g ; g ) are determined.