Abstract
Let [Formula: see text] be a simple vertex operator algebra (VOA) and consider a representation category of [Formula: see text] that is a vertex tensor category in the sense of Huang–Lepowsky. In particular, this category is a braided tensor category. Let [Formula: see text] be an object in this category that is a simple current of order two of either integer or half-integer conformal dimension. We prove that [Formula: see text] is either a VOA or a super VOA. If the representation category of [Formula: see text] is in addition ribbon, then the categorical dimension of [Formula: see text] decides this parity question. Combining with Carnahan’s work, we extend this result to simple currents of arbitrary order. Our next result is a simple sufficient criterion for lifting indecomposable objects that only depends on conformal dimensions. Several examples of simple current extensions that are [Formula: see text]-cofinite and non-rational are then given and induced modules listed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
