2-generated axial algebras of Monster type (2β,β)

Abstract

Axial algebras of Monster type (α,β) are a class of non-associative algebras that includes, besides associative algebras, other important examples such as the Jordan algebras and the Griess algebra. 2-generated primitive axial algebras of Monster type (α,β) naturally split into three cases: the case when α∉{2β,4β}, the case α=4β and α=2β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).