Left-symmetric superalgebra structures on the N = 2 superconformal algebras

ABSTRACT

The super-Virasoro algebras, also known as the superconformal algebras, are nontrivial graded extensions of the Virasoro algebra to Lie superalgebra version. In this paper, we classify the compatible left-symmetric superalgebra structures on the N = 2 Ramond and Neveu–Schwarz superconformal algebras under certain conditions, which generalizes the corresponding results for the Witt, Virasoro and super Virasoro algebras.

KEYWORDS:

• N = 2 Neveu-Schwarz superconformal algebra
• N = 2 Ramond superconformal algebra
• left-symmetric algebra
• left-symmetric superalgebra
• Virasoro algebra

AMS CLASSIFICATION:

• 17B68
• 17B60
• 17D25
• 81R10

Acknowledgement

The authors would like to thank Professor Hongjia Chen for suggestion to this topic. They are grateful to the referee for pointing out many inaccuracies and typos.