Vertex operator superalgebras associated with affine Lie superalgebras

ABSTRACT

It is proved that the induced module $V_{\widehat{𝔤}}(k,0)$ of level k associated with a finite dimensional simple Lie superalgebra 𝔤 with a nondegenerate even supersymmetric invariant bilinear form is a ℤ-graded vertex operator superalgebra, and the explicit expression for the virasoro algebra on any twisted $V_{\widehat{𝔤}}(k,0)$-module is given.

KEYWORDS:

• Affine Lie superalgebra
• twisted module
• vertex operator superalgebra

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B67
• 17B69

Acknowledgements

This paper is written under the direction of Professor Chongying Dong in University of California, Santa Cruz during my visit to him. We would like to express our deep gratitude to him for valuable advice.