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We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $$\mathfrak {sl}(m, n, D)$$sl(m,n,D) when $$m+n \ge 3$$m+n≥3 and D is a superdialgebra,… Click to show full abstract
We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $$\mathfrak {sl}(m, n, D)$$sl(m,n,D) when $$m+n \ge 3$$m+n≥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.
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2017
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