Integrable graded magnets

She solutions to the Yang–Baxter equation are found which are invariant with respect to the general linear and orthosymplectic supergroups. Hamiltonians and higher integrals of motion (transfer matrix) of the corresponding graded spin systems are diagohalized for finite chains. A generalization of the Yang–Baxter equation is formulated for the $\sigma$-commutative $G$-graded Zamolodchikov's algebra. Bibl. – 30.