On Derivation Algebras Of A Heisenberg Superalgebra

In this thesis, we mainly study the some properties of the derivation algebra of Heisenberg superalgebra.In the first part, we assert that a Heisenberg superalgebra could be a central extension of an abelian superalgebra, that is H = g+Fc.In the second part, we discuss some properties of the derivation algebra of a Heisenberg superalgebra from discussing the matrix of D ∈ (DerH)_γ relative to the basis, the main results are as follows:Theorem 1 d ∈ (Derg)_γ could be extent to D ∈ (DerH)_γ(?)d satisfies ψ(d(x_α)x_β) + (-1)^γαψ{x_α,d(x_β)) = k_dψ(x_α,x_β). Here α,β,γ ∈ Z₂.Theorem 2 Let H = g+Fc is a Heisenberg superalgebra, then DerH is not a simple complete Lie Heisenberg superalgebra, but H could be the direct sun of two simple complete ideals.