Universal central extensions of superdialgebras of matrices

Abstract

We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $\mathfrak{sl}(m,n,D)$ when $m+n\ge 3$ and $D$ is a superdialgebra, solving in particular the problem when $D$ is an associative algebra, superalgebra or dialgebra. To accomplish this task we use a different method than the standard studied in the literature. We introduce and use the non-abelian tensor square of Leibniz superalgebras and its relations with the universal central extension.

13 pages

References in corpus (3)

• Non-abelian tensor product and homology of Lie Superalgebras
• Universal central extensions of $s{l}_{m|n}$ over $Z/2Z$-graded algebras
• Universal central extensions of $\mathfrak{sl}(m,n,A)$ of small rank over associative superalgebras