Universal decomposition algebras and the classification of 2-generated non-primitive axial algebras of Jordan type

Abstract: Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive axial algebras also have univesal algebras. Furthermore, by using the existence of a universal algebra, 2-generated non-primitive axial algebras of Jordan type is classified.