On 3-transposition groups generated by $\sigma$-involutions associated to c=4/5 Virasoro vectors

Ching Hung Lam; Hiroshi Yamauchi

On 3-transposition groups generated by $\sigma$-involutions associated to c=4/5 Virasoro vectors

Quantum Algebra 2013-11-13 v1 Mathematical Physics Group Theory math.MP

Authors: Ching Hung Lam , Hiroshi Yamauchi

Abstract

In this paper, we show that $\sigma$ -involutions associated to extendable c=4/5 Virasoro vectors generate a 3-transposition group in the automorphism group of a vertex operator algebra (VOA). Several explicit examples related to lattice VOA are also discussed in details. In particular, we show that the automorphism group of the VOA $V_{K_{12}}^{\hat{\nu}}$ associated to the Coxeter Todd lattice $K_{12}$ contains a subgroup isomorphic to ${}^+\Omega^{-}(8,3)$ .

Keywords

3-transposition groups $\sigma$-involutions Virasoro vectors vertex operator algebras automorphism groups lattice VOA Coxeter Todd lattice

Cite

@article{arxiv.1311.2829,
  title  = {On 3-transposition groups generated by $\sigma$-involutions associated to c=4/5 Virasoro vectors},
  author = {Ching Hung Lam and Hiroshi Yamauchi},
  journal= {arXiv preprint arXiv:1311.2829},
  year   = {2013}
}

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38 pages

On 3-transposition groups generated by $\sigma$-involutions associated to c=4/5 Virasoro vectors

Abstract

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