Derivations from the even parts into the odd parts for Hamiltonian superalgebras

Abstract

Let W 1 and H 0 denote the odd parts of the general Witt modular Lie superalgebra W and the even parts of the Hamiltonian Lie superalgebra H over a field of characteristic p > 3, respectively. We give a torus of H 0 and the weight space decomposition of the special subalgebra of W 1 with respect to the torus. By means of the derivations of the weight 0 and three series of outer derivations from H 0 into W 1 , the derivations from the even parts of Hamiltonian superalgebra to the odd parts of Witt superalgebra are determined.