Classifying 2-generated symmetric axial algebras of Monster type

Abstract

In [15], Yabe gives an almost complete classification of primitive symmetric 2-generated axial algebras of Monster type, leaving open the case of algebras in characteristic 5 and axial dimension larger than 5. In this note, we complete the classification of these algebras, by constructing a new infinite-dimensional primitive 2-generated symmetric axial algebra Hˆ of Monster type (2,12) over a field of characteristic 5, and showing all the cases not falling into Yabe's classification are factors of Hˆ.