The first cohomology of N = 1 super Virasoro algebras

Abstract

In this paper, we determine the first cohomology groups of centerless N = 1 super Virasoro algebras with coefficients in their tensor density modules. As applications, we classify all central extensions and derivations of the complete spectrum-generating superalgebra.

Keywords:

• Central extensions
• super Virasoro algebras
• the first cohomology groups

2010 Mathematics Subject Classification:

• 17B65
• 17B68
• 17B70

Acknowledgments

We gratefully acknowledge the partial financial support from the NSFC (No. 11871249) and the Natural Science Foundation of Shanghai (16ZR1425000).