Local Superderivations of Heisenberg Superalgebras

For an algebraically closed field [Formula: see text] of characteristic different from 2 and a field [Formula: see text] satisfying that for all [Formula: see text], [Formula: see text], [Formula: see text] if and only if [Formula: see text], we extend the notion of superderivations to special graded local superderivations, graded local superderivations and local superderivations. Applying matrix theory, we establish a calculation method for local superderivations. Then we determine all the special graded local superderivations of Heisenberg superalgebras of even center over [Formula: see text]and graded local superderivations and local superderivations of Heisenberg superalgebras of even center over [Formula: see text]. Finally, we determine all the special graded local superderivations, graded local superderivations and local superderivations of Heisenberg superalgebras of odd center over [Formula: see text].