Abstract: | q-Deformations of the Toda chains related to infinite series of Lie algebras and to their affine analogs are described. The corresponding 2×2 L-operators satisfying the standard quadratic algebra of XXZ-type are constructed. In the quantum case, the procedure of separation of variables is described. Bibliography: 14 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 205, 1993, pp. 71–84. Translated by B. M. Bekker. |