Generalization of the $$mathcal{U} $$ q (gl(N)) Algebra and Staggered Models

We develop a technique for the construction of integrable models with a ₂ grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang–Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group , with a matrix deformation parameter q such that (q)² = q². The symmetry behind these models can also be interpreted as the tensor product of the (–1)-Weyl algebra by an extension of _q(gl(N)) with a Cartan generator related to deformation parameter –1.