Simple currents and extensions of vertex operator algebras

Abstract

We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are {\em simple currents} associated with semisimple weight one primary vectors. In the case that the extension is again a vertex operator algebra, the rationality of the extended algebra is discussed. These results are applied to affine Kac-Moody algebras in order to construct all the simple currents explicitly (except for $E_8$) and to get various extensions of the vertex operator algebras associated with integrable representations.

Latex, 41 pages; One important reference is added plus some minor changes

References in corpus (2)

• Representation theory and tensor product theory for vertex operator algebras
• The theory of physical superselection sectors in terms of vertex operator algebra language

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