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arXiv · 1602.04507

Universal central extensions of superdialgebras of matrices

Xabier García-Martínez·Manuel Ladra
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Abstract

We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $\mathfrak{sl}(m, n, D)$ when $m+n \geq 3$ 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.

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Xabier García-Martínez, Manuel Ladra. 2016-02-14. Universal central extensions of superdialgebras of matrices. https://arxiv.org/abs/1602.04507

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