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 HO 0 . Then we determine the homogeneous derivations from HO 0 into W 0 , the even part of the generalized Witt superalgebra W . Finally, we determine the derivation algebra and outer derivation algebra of HO 0 .Derivations for the even part of the odd Hamiltonian superalgebra 2 was determined for the finite-dimensional odd Hamiltonian superalgebra HO. Note that the derivations of the even parts have been studied for the Lie superalgebras of Cartan type W, S, and H (see [5,6]). However, in contrast to the setting of H, we determine completely the derivation space from the even part of HO into the even part of W, and the derivation algebra of the even part of HO, also. This paper is arranged as follows. In Section 1 we introduce the necessary notations, definitions and known results. In Section 2 we first give the generating set of the even part of the odd Hamiltonian superalgebra. Then we determine the nonnegative Z-degree derivations from the even part of the odd Hamiltonian superalgebra into the even part of the generalized Witt superalgebra. In Section 3 we determine the negative Z-degree derivations from the even part of the odd Hamiltonian superalgebra into the even part of the generalized Witt superalgebra. In Section 4 we determine completely the derivation algebra and outer derivation algebra of the even part of the odd Hamiltonian superalgebra.
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