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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 $m+n \geq 3$.

First Page

1552

Last Page

1569

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Mathematics Commons

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