Bazhanov, V. V.Kashaev, R. M.Mangazeev, V. V.Stroganov, Yu G.2026-01-012026-01-010010-3616ORCID:/0000-0001-6017-9231/work/162949691https://hdl.handle.net/1885/733801078We show that the R-matrix which intertwines two n-by-Nn-1 state cyclic L-operators related with a generalization of Uq(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as the R-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genus g=N2(n-1)((n-1)N-n)+1 defined by 2 n-3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of the L-operator and its connection to the SOS models are also discussed.16en199110.1007/BF020994970000969260