On primitive axial decomposition algebras of Majorana type with degenerate eigenvalues

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 $eta otin{0,1,frac{1}{2}}$. This class includes specializations of 2-generated axial algebras of Majorana type $(xi,eta)$ to the case with $xi=eta$.