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

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

2005-10-26

arxiv.org/abs/math/0510567v1

Mathematics

Rings and Algebras

21 pages

Scientific paper

In this paper we consider the derivations for even part of the finite-dimensional Hamiltonian superalgebra $H$ over a field of prime characteristic. We first introduce an ideal $\frak{N}$ of $H_{\bar{0}}$ and show that the derivation space from $H_{\bar{0}}$ into $W_{\bar{0}}$ can be obtained by the derivation space from $\frak{N}$ into $W_{\bar{0}},$ the even part of the generalized Witt superalgebra $W$. For further application we also give the generating set of the ideal $\frak{N}$. Then we describe three series of exceptional derivations from $ {H}_{\bar{0}}$ into $W_{\bar{0}}.$ Finally, we determine all the derivations vanishing on the non-positive $\mathbb{Z}$-graded part of $ H_{\bar{0}}$, the odd $\mathbb{Z}$-homogeneous derivations, and negative $\mathbb{Z}$-homogeneous derivations from ${H}_{\bar{0}}$ into $W_{\bar{0}}.$

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