• Corpus ID: 119123828

Simple current extensions of vertex operator algebras by unitary modules

@article{Lin2017SimpleCE,
  title={Simple current extensions of vertex operator algebras by unitary modules},
  author={Xingjun Lin},
  journal={arXiv: Quantum Algebra},
  year={2017}
}
  • Xingjun Lin
  • Published 12 September 2017
  • Mathematics
  • arXiv: Quantum Algebra
In this paper, a condition making vertex operator superalgebras to be unitary is determined and an analogue of conformal spin-statistics theorem in conformal field theory is proved. As an application of these results, it is proved that under some assumptions there exist vertex operator algebra structures on the direct sum of simple current unitary modules of unitary vertex operator algebras. 
2 Citations

On Infinite Order Simple Current Extensions of Vertex Operator Algebras

We construct a direct sum completion $\mathcal{C}_{\oplus}$ of a given braided monoidal category $\mathcal{C}$ which allows for the rigorous treatment of infinite order simple current extensions of

Loop groups and noncommutative geometry

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective

References

SHOWING 1-10 OF 31 REFERENCES

Simple currents and extensions of vertex operator algebras

We consider how a vertex operator algebra can be extended to an abelian interwining algebra by a family of weak twisted modules which aresimple currents associated with semisimple weight one primary

Twisted representations of vertex operator algebras

This paper gives an analogue of Ag(V) theory for a vertex operator superalgebra V and an automorphism g of finite order. The relation between the g-twisted V-modules and Ag(V)-modules is established.

Rational vertex operator algebras and the effective central charge

We establish that the Lie algebra of weight 1 states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank 1 is bounded above by the effective central charge c~. We

Modularity in Orbifold Theory for Vertex Operator Superalgebras

This paper is about the orbifold theory for vertex operator superalgebras. Given a vertex operator superalgebra V and a finite automorphism group G of V, we show that the trace functions associated

Extension of Vertex Operator Algebras by a Self-Dual Simple Module

Abstract We prove the existence and the regularity of the extension by a self-dual simple current for certain regular vertex operator algebras.

Framed Vertex Operator Algebras, Codes and the Moonshine Module

Abstract:For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge ½, two codes are introduced and studied. It is proved that such vertex

From Vertex Operator Algebras to Conformal Nets and Back

We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure

Virasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory

Abstract A theory of tensor products of modules for a vertex operator algebra is being developed by Lepowsky and the author. To use this theory, one first has to verify that the vertex operator