On primitive axial decomposition algebras of Majorana type with degenerate eigenvalues

Abstract

A class of axial decomposition algebras with Miyamoto group generated by two Miyamoto automorphisms and three eigenvalues $0,1$ and $\eta$ is introduced and classified in the case with $\eta\notin\{0,1,\frac{1}{2}\}$. This class includes specializations of 2-generated axial algebras of Majorana type $(\xi,\eta)$ to the case with $\xi=\eta$.