Universal Central Extensions of Leibniz Superalgebras Over Superdialgebras

Abstract

We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of sl(m, n, D) when 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.2010 Mathematics Subject Classification. 17B60, 17B55, 17B05.