A Class of Finite-dimensional Lie Superalgebras of Hamiltonian Type

Abstract

A class of finite-dimensional Cartan-type Lie superalgebras H(n,m) over a field of prime characteristic is studied in this paper. We first determine the derivation superalgebra of H(n,m). Then we obtain that H(n,m) is restrictable and it is an extension of the Lie superalgebra [Formula: see text]. Finally, we prove that H(n,m) is isomorphic to a subalgebra of the restricted Hamiltonian Lie superalgebra [Formula: see text].