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

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 generator set of $H{O}_{\bar{0}}\mathrm{.}$ Then we determine the homogeneous derivationsfrom $H{O}_{\bar{0}}$ into $W_{\bar{0}},$ the even part of the generalized Witt superalgebra $W$. Finally, wedetermine the derivation algebra and outer derivation algebra of $H{O}_{\bar{0}}\mathrm{.}$