Central extensions, derivations, and automorphisms of the super Heisenberg-Virasoro algebra

In this paper, we use the Balinsky-Novikov construction to naturally realize the super Heisenberg-Virasoro algebra g. We then proceed to compute the second cohomology of g with trivial coefficients and determine its universal central extension. This yields two odd 2-cocycles in addition to the Virasoro 2-cocycle. We also calculate the first cohomology group of g in the adjoint module to classify all derivations of g. Finally, we classify all automorphisms of g and describe its automorphism group.