Remarks on the Second Homology Groups of Queer Lie Superalgebras

Abstract

The aim of this note is to completely determine the second homology group of the special queer Lie superalgebra $\mathfrak{sq}_n(R)$ coordinatized by a unital associative superalgebra $R$, which will be achieved via an isomorphism between the special linear Lie superalgebra $\mathfrak{sl}_{n}(R\otimes Q_1)$ and the special queer Lie superalgebra $\mathfrak{sq}_n(R)$.