On the classification of 2-generated axial algebras of Majorana type

A class of axial algebras generated by two axes with eigenvalues 0, 1, η and ξ called axial algebras of Majorana type is introduced and classified when they are 2-generated, over fields of characteristics neither 2 nor 5 and there exists an automorphism switching generating axes. The class includes deformations of nine Norton-Sakuma algebras. Over fields of characteristics 5, the axial algebras of Majorana type with the axial dimension at most 5 are classified.