Abstract:
We deal with adjoint commutator and Jordan algebras of isotopes of prime strictly $(-1,1)$-algebras. It is proved that a system of identities of the form $[x_1,x_2,x_2,x_3,\dots,x_n]$ for $n=2,\dots,5$ is discernible on isotopes of prime $(-1,1)$-algebras. Also it is shown that adjoint Jordan algebras for suitable isotopes of prime $(-1,1)$-algebras may possess distinct sets of identities. In particular, isotopes of a prime Jordan monster have different sets of identities in general.
Keywords:right alternative algebra, strictly $(-1,1)$-algebra, Jordan algebra, prime algebra, isotope, homotope, identity, Lie nilpotence.