Lagrangian extensions and left-symmetric structures on the four-dimensional real Lie superalgebras

UDC 512.81; 512.55 Over real numbers, Backhouse classified all four-dimensional Lie superalgebras. From this list, we investigate the Lie superalgebras that can be obtained as Lagrangian extensions. Moreover, we study left-symmetric structures on these Lie superalgebras. Furthermore, except two of them, we show that they are all Novikov superalgebras.