2-generated axial algebras of Monster type

We provide the basic setup for the project, initiated by Felix\r\nRehren, aiming at classifying all 2-generated axial algebras of\r\nMonster type (α,β) over a field F. Using this, we first show\r\nthat every such algebra has dimension at most 8, except for\r\nthe case (α, β) = (2, 12 ), where the Highwater algebra provides\r\nexamples of dimension n, for all n ∈ N ∪ {∞}. We then\r\nclassify all 2-generated axial algebras of Monster type (α,β)\r\nover Q(α,β), for α and β algebraically independent over Q.\r\nFinally, we generalise the Norton-Sakuma Theorem to every\r\nprimitive 2-generated axial algebra of Monster type (1/4, 1/32 ) \r\nover a field of characteristic zero, dropping the hypothesis on the existence of a Frobenius form.