3-Transposition Groups of Symplectic Type and Vertex Operator Algebras

TL;DR

This paper classifies certain 3-transposition groups acting on vertex operator algebras with specific symmetry and positivity conditions, extending previous classifications and exploring related applications.

Contribution

It generalizes and refines the classification of 3-transposition groups acting on VOAs under new assumptions, broadening understanding of their structure.

Findings

Classification of centerfree 3-transposition groups acting on VOAs

Extension of previous results by Kitazume and Miyamoto

Application to related algebraic structures

Abstract

The 3-transposition groups that act on a vertex operator algebra in the way described by Miyamoto are classified under the assumption that the group is centerfree and the VOA carries a positive-definite invariant Hermitian form. This generalizes and refines the result of Kitazume and Miyamoto. Application to a similar but different situation is also considered in part by a slight generalization of the argument.