Griess algebras generated by 3 Ising vectors of central 2A-type

AbstractWe study the Griess algebra generated by three Ising vectors e,f, and g in a CFT type vertex operator algebra V with V1=0 such that 〈e,f〉=〈e,g〉=132. We call such a configuration of central 2A-type. Under this assumption, we show that there are only 5 possible structures of Griess algebras and they correspond exactly to the Griess algebras GVB(nX) of the five VOA VB(nX), nX∈{1A,2B,3A,4B,2C}, constructed by Höhn–Lam–Yamauchi