3-transposition groups arising in VOA theory

TL;DR

This paper reviews the role of 3-transposition groups in vertex operator algebra theory, highlighting their construction via Matsuo algebras and identifying groups that do not arise from this method.

Contribution

It provides a survey of 3-transposition groups in VOA theory and presents examples of groups not obtainable through Matsuo algebras.

Findings

Some 3-transposition groups are automorphism groups of VOAs.

Not all 3-transposition groups can be constructed from Matsuo algebras.

Examples of such groups and their associated VOAs are provided.

Abstract

We review 3-transposition groups arising in vertex operator algebra theory. One can construct a commutative algebra called the Matsuo algebra out of a 3-transposition group. Some 3-transposition groups arise as automorphism groups of vertex operator algebras via Matsuo algebras but there exist some 3-transposition groups which do not arise through Matsuo algebras. We will exhibit examples of those groups together with VOAs. This article is based on the author's talk at the seminar on ``Majorana, Axial, Vertex Algebras and the Monster (MAVAM)'' held online on June 4th, 2021.