SOLID LINES IN AXIAL ALGEBRAS OF JORDAN TYPE 21 AND JORDAN ALGEBRAS

We show that a primitive axial algebra of Jordan type 21 is a Jordan algebra if and only if every 2-generated subalgebra is solid, a notion introduced recently by Ilya Gorshkov, Sergey Shpectorov and Alexei Staroletov. As a byproduct, we show that a subalgebra generated by axes a, b is solid if and only if the associator [La,Lb] is a derivation. Moreover, we show that 2-generated subalgebras that are not solid contain precisely 3 axes.