New solutions to the image-invariant Yang–Baxter equations at roots of unity Original Research Article

We find new solutions to the Yang–Baxter equations with the R-matrices possessing image symmetry at roots of unity, using indecomposable representations. The corresponding quantum one-dimensional chain models, which can be treated as extensions of the XXZ model at roots of unity, are investigated. We consider the case image. The Hamiltonian operators of these models as a rule appear to be non-Hermitian. Taking into account the correspondence between the representations of the quantum algebra image and the quantum super-algebra image, the presented analysis can be extended to the latter case for the appropriate values of the deformation parameter.