Local Superderivations Of Heisenberg Lie Superalgebras

Let IF be an algebraically closed field of characteristic different from 2 and R a real field.In this paper,we extend the notion of superderivations to the ones of special graded local superderivations,graded local superderivations and local su-perderivations,respectively.Applying matrix theory and classification of Heisenberg superalgebra,we establish a calculation method for local superderivations.Then we determine all the special graded local superderivations of Heisenberg superalgebras of even center over IF and graded local superderivations and local superderivations of Heisenberg superalgebras of even center over R.Finally,we determine all the special graded local superderivations,graded local superderivations and local su-perderivations of Heisenberg superalgebras of odd center over IF.