Polynomial identities of RA and RA2 loop algebras

Let F be an algebraically closed field of characteristic zero and L an RA loop. We prove that the loop algebra FL is in the variety generated by the split Cayley-Dickson algebra Z(F) over F. For RA2 loops of type M(Dib(A),(-1), g(0)), we prove that the loop algebra is in the variety generated by the algebra A(3) which is a noncommutative simple component of the loop algebra of a certain RA2 loop of order 16. The same does not hold for the RA2 loops of type M(G,(-1), g(0)), where G is a non-Abelian group of exponent 4 having exactly 2 squares.