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

The universal central extensions and their extension kernels of the smatrix Lie superalgebra 𝔰𝔩(m, n, 𝒜), the Steinberg Lie superalgebra 𝔰𝔩(m, n, 𝒜) in category SLeib of Leibniz superalgebras are determined under a weak assumption (compared with Mikhalev and Pinchuk, 2000 Mikhalev , A. V. , Pinchuk , I. A. ( 2000 ). Universal central extension of the matrix Lie superalgebras sl(m, n, A) . Contemp. Math. 264 : 111 – 126 . [Google Scholar]) using the first Hochschild homology and the first cyclic homology group.