Turkish Journal of Mathematics
DOI
10.3906/mat-1604-34
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 $m+n \geq 3$.
Keywords
Lie superalgebras, Steinberg superalgebras, universal central extensions
First Page
1552
Last Page
1569
Recommended Citation
GARCÍA-MARTÍNEZ, XABIER and LADRA, MANUEL
(2017)
"Universal central extensions of $\mathfrak{sl}(m, n, A)$ over associative superalgebras,"
Turkish Journal of Mathematics: Vol. 41:
No.
6, Article 15.
https://doi.org/10.3906/mat-1604-34
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss6/15
