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 $\mathfrak{s}{\mathfrak{q}}_n(R)$ coordinatized by a unital associative superalgebra R, which will be achieved via an isomorphism between the special linear Lie superalgebra $\mathfrak{s}{\mathfrak{l}}_n(R\otimes Q_1)$ and the special queer Lie superalgebra $\mathfrak{s}{\mathfrak{q}}_n(R).$

Keywords:

• Central extension
• cyclic homology group
• queer Lie superalgebra
• root-graded Lie superalgebra

2020 Mathematics Subject Classification:

• 17B05
• 19D55

Additional information

Funding

Zhihua Chang was supported by National Natural Science Foundation of China (Nos. 11771455 and 12071150) and Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515011417). Yongjie Wang also thanks the support of National Natural Science Foundation of China (Nos. 11901146 and 12071026) and the Fundamental Research Funds for the Central Universities (No. JZ2021HGTB0124).