Negative $\mathbb{Z}$-Homogeneous Derivations for Even Parts of Odd Hamiltonian Superalgebras
Received:January 15, 2012  Revised:September 03, 2012
Key Words: generalized Witt superalgebra   odd Hamiltonian superalgebra   derivation space.
Fund Project:Supported by the Scientific Research Fund of Heilongjiang Provincial Education Department (Grant No.12521114), the Science Foundation for Young Scholars, Harbin University of Science and Technology (Grant No.2011YF006), the National Natural Science Foundation of China (Grant No.11171055) and the Natural Science Foundation for Distinguished Young Scholars of Heilongjiang Province (Grant No.JC201004).
 Author Name Affiliation Xiuying HUA School of Applied Sciences, Harbin University of Science and Technology, Heilongjiang 150080, P. R. China Wende LIU School of Mathematical Sciences, Harbin Normal University, Heilongjiang 150025, P. R. China
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In this paper we mainly study the negative $\mathbb{Z}$-homogeneous derivations from the even part of the finite-dimensional odd Hamiltonian superalgebra $HO$ into the odd part of generalized Witt superalgebra $W$ over a field of prime characteristic $p>3.$ Using the generating set of $\mathcal{HO},$ by means of calculating actions of derivations on the generating set, we first compute the derivations of $\mathbb{Z}$-degree ${-1},$ then determine the derivations of $\mathbb{Z}$-degree less than ${-1}.$