Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24

Details Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24 Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24

2010-10-26

arxiv.org/abs/1010.5303v2

Mathematics

Quantum Algebra

46 pages

Scientific paper

In 1993, Schellekens obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with central charge 24. However, not all cases are known to exist. The aim of this article is to construct new holomorphic vertex operator algebras using the theory of framed vertex operator algebras and to determine the Lie algebra structures of their weight one subspaces. In particular, we study holomorphic framed vertex operator algebras associated to subcodes of the triply even codes $\RM(1,4)^3$ and $\RM(1,4)\oplus \EuD(d_{16}^+)$ of length 48. These vertex operator algebras correspond to the holomorphic simple current extensions of the lattice type vertex operator algebras $(V_{\sqrt{2}E_8}^+)^{\otimes 3}$ and $V_{\sqrt{2}E_8}^+\otimes V_{\sqrt{2}D_{16}^+}^+$. We determine such extensions using a quadratic space structure on the set of all irreducible modules $R(W)$ of $W$ when $W= (V_{\sqrt{2}E_8}^+)^{\otimes 3}$ or $V_{\sqrt{2}E_8}^+\otimes V_{\sqrt{2}D_{16}^+}^+$. As our main results, we construct seven new holomorphic vertex operator algebras of central charge 24 in Schellekens' list and obtain a complete list of all Lie algebra structures associated to the weight one subspaces of holomorphic framed vertex operator algebras of central charge 24.

Affiliated with

Also associated with

No associations

Rating

Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-159048