Universal central extensions of superdialgebras of matrices

2016/02/14 by Xabier García‐Martínez, García-Martínez, Xabier, M. Ladra +1
Computer Science · Mathematics · #17B05 #17B55 #17B60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1602.04507

openalex publication_date 2016/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of \mathfraksl(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.

Citations

• Universal enveloping algebras of Leibniz algebras and (co)homology

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