Simple current extensions beyond semi-simplicity

Creutzig T, Kanade S, Linshaw AR (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Communications in Contemporary Mathematics World Scientific Publishing

Book Volume: 22

Article Number: 1950001

Journal Issue: 1

DOI: 10.1142/S0219199719500019

Abstract

Let V be a simple vertex operator algebra (VOA) and consider a representation category of V that is a vertex tensor category in the sense of Huang-Lepowsky. In particular, this category is a braided tensor category. Let J 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 V ⊕ J is either a VOA or a super VOA. If the representation category of V is in addition ribbon, then the categorical dimension of J 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 C2-cofinite and non-rational are then given and induced modules listed.

Authors with CRIS profile

Thomas Creutzig

Involved external institutions

University of Alberta CA Canada (CA) University of Denver US United States (USA) (US)

How to cite

APA:

Creutzig, T., Kanade, S., & Linshaw, A.R. (2020). Simple current extensions beyond semi-simplicity. Communications in Contemporary Mathematics, 22(1). https://doi.org/10.1142/S0219199719500019

MLA:

Creutzig, Thomas, Shashank Kanade, and Andrew R. Linshaw. "Simple current extensions beyond semi-simplicity." Communications in Contemporary Mathematics 22.1 (2020).

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