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 ${\mathfrak{sq}}_n(R)$.