- Turkish Journal of Mathematics
- Vol: 41 Issue: 6
- Universal central extensions of sl(m, n, A) over associative superalgebras
Universal central extensions of sl(m, n, A) over associative superalgebras
Authors : Xabier García-martínez, Manuel Ladra
Pages : 1552-1569
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Publication Date : 9999-12-31
Article Type : Makaleler
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