Universal Central Extensions of the Matrix Leibniz Superalgebras sl(m, n, A)

Abstract

The universal central extensions and their extension kernels of the matrix Lie superalgebra sl(m, n, A), the Steinberg Lie superalgebra st(m, n, A) in category SLeib of Leibniz superalgebras are determined under a weak assumption (compared with MP) using the first Hochschild homology and the first cyclic homology group.