Algebras with one of the following identities are considered:rn[[t_1,t_2],t_3} + [[t_2, t_3], t_1] + [[t_3, t_1],t_2] = 0,rn[t_1,t_2]t_3 + [t_2,t_3]t_1 + [t_3,t_1]t_2 =0, {{t_1,t_2],t_3} + {[t_2,t_3} + {[t_3,t_1],t_2} = 0,rnwhere [t_1,t_2] = t_1t_2 -t_2t_1 and {t_1,t_2} = t_1t_2 + t_2t_1. We prove that any algebra with a skew-symmetric identity of degree 3 is isomorphic or anti-isomorphic to one of such algebras or can be obtained as their q-commutator algebras.
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