Leibniz central extensions of Lie superalgebras

Abstract

In this paper, we develop a general theory on Leibniz central extensions of Lie superalgebras and apply it to determine the second Leibniz cohomology groups for several classes of Lie superalgebras, including classical Lie superalgebras, Neveu–Schwarz superalgebras, differentiably simple Lie superalgebras, and affine (toroidal) Kac–Moody Lie superalgebras.