Turkish Journal of Mathematics
Abstract
We find the universal central extension of the matrix superalgebras $\mathfrak{sl}(m, n, A)$, where $A$ is an associative superalgebra and $m+n = 3, 4$, and its relation with the Steinberg superalgebra $\mathfrak{st}(m, n,A)).$ We calculate $H_2$ $(\mathfrak{sl}(m, n,A))$ and $H_2$ $(\mathfrak{st}(m, n,A))$. Finally, we introduce a new method using the nonabelian tensor product of Lie superalgebras to and the connection between $H_2$ $(\mathfrak{sl}(m, n, A))$ and the cyclic homology of associative superalgebras for $m+n \geq 3$.
DOI
10.3906/mat-1604-34
Keywords
Lie superalgebras, Steinberg superalgebras, universal central extensions
First Page
1552
Last Page
1569
Recommended Citation
GARCÍA-MARTÍNEZ, X, & LADRA, M (2017). Universal central extensions of $\mathfrak{sl}(m, n, A)$ over associative superalgebras. Turkish Journal of Mathematics 41 (6): 1552-1569. https://doi.org/10.3906/mat-1604-34
